- Shinichiro Akiyama (Institute for Physics of Intelligence, The University of Tokyo)
- "Tensor renormalization group approach to the four-dimensional lattice gauge theories"
[Abstract] [pdf]
Abstract
The tensor renormalization group (TRG) is a typical tensor network approach to investigate the path integrals of lattice field theories. The TRG can be seen as a variant of the real-space renormalization group and allows us to approximately contract a tensor network representing the original path integral. This approach does not resort to any probabilistic interpretation for the Boltzmann weight and it has been confirmed that the TRG allows us to access various lattice theories with the sign problem. In addition, the TRG is one of the promising tensor network methods to investigate the four-dimensional lattice field theories. In this talk, reviewing the current status of the TRG approach in higher-dimensional applications, we explain the latest TRG study of Zn gauge-Higgs models at finite density with n=2,3. In particular, we show that we can determine the critical endpoints, evaluating the thermodynamic quantities even at finite density by the TRG.
- Jeanne Colbois (Laboratoire de Physique Théorique, Université de Toulouse)
- "Extreme value statistics in random spin chains"
[Abstract] [pdf]
Abstract
Extreme value theory is best known to predict disasters, for example in hydrology to anticipate floods or in epidemiology to quickly identify emerging diseases. Here, I will describe how it gives insight into some non-trivial effects in random spin chains. Indeed, despite a very good understanding of single-particle Anderson localization in one-dimension, many-body effects are still full of surprises. A famous example is the interaction-driven many-body localization (MBL) [1,2] in the random-field Heisenberg chain, whose non-interacting limit already shows non-trivial multiparticle physics, which allows to probe some general mechanisms using large-scale exact diagonalization. Here, I would like to discuss in particular a chain breaking mechanism occurring in the XX and the Heisenberg (XXX) spin chains in a random field from an extreme value statistics perspective [3]. Supported by state-of-the-art numerical simulations at infinite temperature, this analysis leads to the striking observation of a sharp "extreme-statistics transition" in the Heisenberg chain as the disorder changes, which may coincide with the recently debated MBL transition. If time allows, I will discuss some connections to other occurrences of extreme value statistics in disordered interacting systems.
[1] D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, “Many-body localization, thermalization, and entanglement”, Rev. Mod. Phys. 91, 021001 (2019)
[2] F. Alet and N. Laflorencie, “Many-body localization: An introduction and selected topics”, Comptes Rendus Physique 19, 498 (2018)
[3] J. Colbois and N. Laflorencie, “Breaking the chains: extreme value statistics and localization in random spin chains”, arXiv:2305.10574 (2023)
- Daichi Kagamihara (Department of Physics, Kindai University)
- "Quench Dynamics of Rényi Entanglement Entropy in Non-Interacting and Strongly-Interacting Bosons"
[Abstract] [pdf]
Abstract
We investigate the time evolution of the Rényi entanglement entropy of bosons in an optical lattice following quantum quenches. Notably, an experimental method exists for measuring the Rényi entanglement entropy in this system [1]. Our study focuses on two distinct regimes where we derive analytical results: a non-interacting limit [2] and a strongly-interacting region [3].
In the non-interacting case, starting from insulating product states, we find that the Rényi entanglement entropy is characterized by the permanent of a matrix comprising time-dependent single-particle correlation functions. This finding enables simulations of significantly larger systems than those manageable by conventional methods such as the exact diagonalization method.
In the strongly-interacting case, taking an initial state as the Mott-insulating state, we explore the dynamics induced by a slight increase in hopping amplitude. Low-energy excited states are well described by fermionic quasi-particles known as doublons and holons, which are excited in the form of entangled pairs by the quench. We establish an analytical expression of the Rényi entanglement entropy in terms of the correlation functions associated with these quasiparticles. Furthermore, we provide a physical interpretation of the behavior of the Rényi entanglement entropy based on the derived expression.
[1] R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin, M. Rispoli, and M. Greiner, Nature (London) 528, 77 (2015); A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Science 353, 794 (2016).
[2] D. Kagamihara, R. Kaneko, S. Yamashika, K. Sugiyama, R. Yoshii, S. Tsuchiya, I. Danshita, Phys. Rev. A 107, 033305 (2023).
[3] S. Yamashika, D. Kagamihara, R. Yoshii, S. Tsuchiya, arXiv:2209.13340.
- Ying-Jer Kao (Department of Physics and Center for Theoretical Physics, National Taiwan University)
- "Emergence of a Dirac spin liquid state in the spin-1/2 AF kagome Heisenberg mode: a symmetric tensor network study"
- Hosho Katsura (Department of Physics, The University of Tokyo)
- "Integrable SYK models"
[Abstract] [pdf]
Abstract
We introduce and study integrable variants of Sachdev-Ye-Kitaev (SYK) models with and without supersymmetry. In both cases, the ground states of the models exhibit anomalous properties. If time allows, we also discuss the dynamical properties of the models.
- Masaki Oshikawa (Institute for Solid State Physics, The University of Tokyo)
- "Construction of Symmetry-Protected Topological Phases with Duality Transformations"
- Frank Pollmann (TUM School of Natural Sciences, Technical University of Munich)
- "Isometric Tensor Networks: Efficient numerical simulations and exact representation of quantum states"
[Abstract]
Abstract
We investigate the class of isometric tensor network states (isoTNSs), which generalize the isometry condition of one-dimensional matrix-product states to tensor networks in higher dimensions. Notably, the isometry condition allows for both efficient classical simulation and a simple sequential preparation on quantum computers. First, we benchmark the variational power of isoTNS for finding ground states of local Hamiltonians and performing time evolution. Second, we identify model systems that have exact isoTNS representable ground states.
- Takahiro Sagawa (Department of Applied Physics, The University of Tokyo)
- "On the existence of complete thermodynamic potentials: a resource-theoretic approach"
[Abstract]
Abstract
In equilibrium thermodynamics, the Boltzmann entropy serves as a complete thermodynamic potential that characterizes state convertibility in a necessary and sufficient manner. In this talk, I will present our result [1,2] that a complete thermodynamic potential emerges for quantum many-body systems under physically reasonable assumptions, even in out-of-equilibrium and fully quantum situations. Our proof is based on the resource-theoretic formalism of thermodynamics and the quantum ergodic theorem. The complete thermodynamic potential is in general given by a quantity called the spectral divergence rate, while under some assumptions it reduces to the Kullback-Leibler (KL) divergence rate. In addition, I will discuss the case where an auxiliary system called a catalyst is introduced, and show that the KL divergence again serves as a complete thermodynamic potential if a small amount of correlation is allowed between the system and the catalyst [3].
[1] P. Faist, T. Sagawa, K. Kato, H. Nagaoka, and F. G. S. L. Brandao, Phys. Rev. Lett. 123, 250601 (2019).
[2] T. Sagawa, P. Faist, K. Kato, K. Matsumoto, H. Nagaoka, and F. G. S. L. Brandao, J. Phys. A: Math. Theor. 54, 495303 (2021)
[3] N. Shiraishi and T. Sagawa, Phys. Rev. Lett. 126, 150502 (2021).
- Kazuhiro Seki (Quantum Computational Science Research Team, RIKEN Center for Quantum Computing)
- "Quantum-classical hybrid method for microcanonical ensembles"
[Abstract] [pdf]
Abstract
We propose a method to calculate finite-temperature properties of many-body systems for microcanonical ensembles, which may find a potential application of near-term quantum computers [1]. In our formalism, a microcanonical ensemble is specified with a target energy and a width of the energy window, by expressing the density of states as a sum of Gaussians centered at the target energy with its spread associated with the width of the energy window. Using the Fourier representation of the Gaussian, we then show that thermodynamic quantities such as entropy and temperature can be calculated by evaluating the trace of the time-evolution operator, and the trace of the time-evolution operator multiplied by the Hamiltonian of the system. We also describe how these traces can be evaluated using random diagonal-unitary circuits suitable for quantum computation. We demonstrate the proposed method by numerically calculating thermodynamic quantities of the one-dimensional spin-1/2 Heisenberg model on small clusters and show that the proposed method is most effective for the target energy around which a larger number of energy eigenstates exist.
[1] K. Seki and S. Yunoki, Phys. Rev. B 106, 155111 (2022).
- Hiroshi Shinaoka (Department of Physics, Saitama University)
- "Tensorizing Feynman diagrams: quantics tensor trains and quantics tensor cross interpolation"
[Abstract] [pdf]
Abstract
Correlation functions of quantum systems---central objects in quantum field theories---are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, hindering the application of sophisticated many-body theories to interesting problems. In this talk, we review recently proposed two ideas: a multi-scale space-time ansatz [1] for correlation functions of quantum systems based on quantics tensor trains, and quantics tensor cross interpolation [2]. In the QTT approach, we tensorize the space-time dependence of a correlation function by using "qubits'' describing exponentially different length scales. The ansatz then assumes a separation of length scales by decomposing the resulting high-dimensional tensors into tensor trains (known also as matrix product states). We numerically verify the ansatz for various equilibrium and nonequilibrium systems and demonstrate compression rates of several orders of magnitude for challenging cases. Essential building blocks of diagrammatic equations, such as convolutions or Fourier transforms, are formulated in the compressed form. In the quantics tensor cross interpolation (QTCI) [2], we combine the quantics representation and tensor cross interpolation. QTCI allows us to construct a QTT representation of a multivariate function, e.g., a correlation function, at a computation cost that scales only linearly with the number of bits. To demonstrate the potential power of QTCI, we apply QTCI to the computation of Brillouin zone integrals, e.g., Chern numbers. Finally, if time is allowed, we introduce our recent applications of QTT and QTCI to weak coupling expansions for multiorbital quantum impurity models.
References
[1] H. Shinaoka et al., Phys. Rev. X 13, 021015 (2023).
[2] M. K. Ritter, Y. N. Fernández, M. Wallerberger, J. von Delft, H. Shinaoka, X. Waintal, arXiv:2303.11819.
- Adam Smith (School of Physics and Astronomy, University of Nottingham)
- "Entanglement Transitions in Unitary Circuit Games"
[Abstract]
Abstract
Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: The “entangler” applies a random local unitary gate with the aim of generating extensive (volume law) entanglement. The “disentangler”, based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general U (4) unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate, which have similar properties that can be understood through a connection to the stochastic Fredkin chain. In contrast, the entangler always wins when using Haar random unitary gates and we observe extensive, volume law entanglement for all non-zero rates of entangling.
reference: arXiv:2304.12965
- Masafumi Udagawa (Department of Physics, Gakushuin University)
- "Local manipulation of Majorana zero mode in Kitaev's chiral spin liquid"
[Abstract]
Abstract
Kitaev's spin liquid is drawing considerable attention as a realistic stage of the quantum spin liquid phase. Among its fascinating properties, the field-induced chiral spin liquid (CSL) state deserves special attention, where the half-integer uantization of thermal Hall conductivity is theoretically predicted, and is experimentally reported for one of the candidate materials, alpha-RuCl3 [1]. The appearance of Majorana zero mode (MZM) is another surprising aspect of the CSL phase. A fractional excitation called vison accompanies MZM and behaves as a non-Abelian Ising anyon. The existence of MZM implies a strange non-locality of the CSL state, where one quantum bit is fractionalized, and associated quantum information can be stored nonlocally. In this talk, towards the real-space control of MZM, we consider the response of Kitaev's spin liquid to local perturbations. In particular, we consider the Kitaev’s honeycomb model in a magnetic field, and address its magnetic and charge responses through the dynamical spectroscopy [2,3]. On the basis of the obtained response functions, we propose a protocol to detect visons through the scanning tunneling microscopy [4]. We further introduce our recent attempt to control visons with external probes [5], and the application to quantum computation [6].
[1] Y. Kasahara et al., Nature 559, 227 (2018).
[2] M. Udagawa, Phys. Rev. B 98, 220404(R) (2018).
[3] M. Udagawa, Journal of Physics: Condensed Matter 33, 254001 (2021).
[4] M. Udagawa, S. Takayoshi and T. Oka, Phys. Rev. Lett. 126, 127201 (2021).
[5] M. Udagawa, S. Takayoshi and T. Oka, in preparation.
[6] M. O. Takahashi, M. G. Yamada, M. Udagawa, T. Mizushima and S. Fujimoto, arXiv:2211.13884.
- Laurens Vanderstraeten (Department of Physics and Astronomy, University of Ghent)
- "Spin liquids and tensor networks"
[Abstract]
Abstract
Spin liquid wavefunctions such as the RVB state are naturally represented in the language of tensor networks. On the one hand, this allows for a thorough investigation of the entanglement properties of these states. On the other, it suggests that tensor networks are very useful as variational parametrizations for the spin liquid ground states of realistic model hamiltonians. This, in turn, would allow for efficient numerical simulations of the phase diagrams and low-energy dynamics of these hamiltonians. In this talk, I will review some of the recent insights in the entanglement properties of spin liquids and new results on the numerical exploration of phase diagrams. I will discuss the case of chiral spin liquids in some detail, for which the situation is more complicated but also more interesting.
- Sylvain Capponi (Toulouse University)
- "Quantum Electrodynamics as the Organizing Principle of Triangular Antiferromagnets"
[Abstract] [pdf]
Abstract
Quantum electrodynamics in 2 + 1 dimensions (QED3) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated J1-J2 Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED3, in the quantum spin liquid regime. This includes a large manifold of explicitly constructed monopole and bilinear excitations of QED3. Ref: A. Wietek, S. Capponi, A. Läuchli, preprint arXiv:2303.01585
- Matthias Gohlke (Okinawa Institute of Science and Technology)
- "Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev spin liquid state"
[Abstract]
Abstract
We show that the matrix product state (MPS) provides a thermal quantum pure state (TPQ) representation in equilibrium in two spatial dimensions over the entire temperature range. We use the Kitaev honeycomb model as a prominent, non-trivial example hosting a quantum spin liquid (QSL) ground state. Our method is able to qualitatively capture the double-peak in the specific heat, which was previously obtained nearly exactly using a method tailored to the Kitaev honeycomb model. In contrast, our method can be applied to general systems including those with competing interactions. We also demonstrate, that the truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state with very low statistical errors.
- Chang-Tse Hsieh (National Taiwan University)
- "Generalized Lieb-Schultz-Mattis theorem for 1d quantum magnets"
[Abstract]
Abstract
The Lieb-Schultz-Mattis (LSM) theorem is a fundamental result in condensed matter physics that relates symmetries to the ground state properties of quantum many-body systems. The conventional LSM theorem states that a 1d antiferromagnetic spin chain with spin-rotation and lattice-translation symmetries cannot have a unique gapped ground state if the spin per unit cell is half-integral. In this talk, I will present extensions of the LSM theorem for 1d quantum magnets with certain combinations of spin-rotation, spatial, and time-reversal symmetries. Our results can be applied to a wider range of systems with spin interactions beyond the Heisenberg exchange interaction, such as Dzyaloshinskii-Moriya and chiral three-spin interactions.
- Masataka Kawano (Department of Physics, Technical University of Munich)
- "Unconventional relaxation dynamics in a constraint electron system on the kagome lattice"
[Abstract] [pdf]
Abstract
Constraints in many-body systems often lead to anomalously slow diffusive dynamics of global conserved quantities at late times. Alghouth there are some intriguing classes of materials in this context such as spin-ice systems, the exploration of the constraint dynamics is far from complete compared to the diversity of materials, highlighting the need for further investigations and discoveries. Here, we show that the interplay between strong electron correlations and geometrical frustration naturally gives rise to a novel class of constraints and associated unconventional relaxation dynamics. We consider the strong-coupling limit of an extended Hubbard model on the kagome lattice, where strong correlations lead to charge subsystem symmetries and dynamically moving sublattice patterns, serving as exotic constraints. Employing a cellular automaton circuit with the constraints, we numerically identify the unconventional charge and spin diffusions with spatially modulated profiles, which manifest as characteristic spectral distributions in dynamic structure factors that can be detected by inelastic neutron scattering experiments on relevant materials. We also provide phenomenological arguments to explain how these unconventional diffusions emerge from the constraints. In particular, we find that spin dynamics are confined within a dynamically moving sublattice, leading to the substantial deviation from a conventional spin diffusion.
- Giacomo Marmorini (Nihon University)
- "Possible measurement of entanglement in a many-body quantum simulator via spiral quantum state tomography"
[Abstract]
Abstract
Spiral quantum state tomography is an efficient protocol of reconstruction of the density matrix, particularly tailored for cold-atom quantum simulators since it does not require single-atom addressing. After a general introduction, we will try to illustrate whether it is possible, in various experimental conditions, to measure certain entanglement properties of interesting many-body quantum states, such as entanglement entropy, with adequate accuracy and what kind of information can be obtained with realistic small-size systems.
- Sanjay Moudgalya (California Institute of Technology)
- "Symmetries as Ground States of Local Hamiltonians"
[Abstract] [pdf]
Abstract
The study of symmetry lies at the heart of various parts of physics. In equilibrium physics, symmetries are useful in classifying phases of matter and in non-equilibrium physics, they are necessary to understand the phenomenon of thermalization. Most symmetries conventionally studied in the literature are examples of so-called on-site unitary symmetries, which have a nice group structure. While such symmetries are sufficient to explain several physical phenomena, recent discoveries of dynamical phenomena collectively known as weak ergodicity breaking have called for a generalization of the notion of symmetry. In this talk, I will discuss the physics of weak ergodicity breaking, particularly phenomena known as quantum many-body scars and Hilbert space fragmentation, and how it motivates a general mathematical framework to define symmetries in quantum many-body systems based on von Neumann algebras. This framework leads to a generalization of the notion of symmetry beyond the conventional ones, provides precise explanation of weak ergodicity breaking in terms of unconventional symmetries, unifies the study of various different dynamical phenomena in the literature, and also opens up several questions on the nature of symmetry in quantum many-body physics.
- Geet Rakala (Okinawa Institute of Science and Technology)
- "Entanglement in random transverse field Ising models"
[Abstract]
Abstract
We perform an efficient numerical strong disorder renormalisation to study entanglement properties of random transverse field Ising models. In particular we look at the random partition entanglement entropy whose bounds can be calculated from number operator fluctuations of the corresponding fermionic model.
- Yasuhiro Shimizu (Department of Physics, Nagoya University)
- "Quantum spin liquid on frustrated magnets"
[Abstract]
Abstract
I will present experimental NMR studies on Kitaev quantum spin liquid and the related materials.
- Rongyang Sun (RIKEN Center for Computational Science)
- "Scalable quantum simulation for topological quantum phases on noisy quantum devices"
[Abstract] [pdf]
Abstract
Topological quantum phases emerge from correlated quantum many-body systems containing novel features such as nontrivial entanglement structure and mutual statistics. However, the co-emerged exponential computational complexity strongly hampers the research of these systems using classical computers. Present booming quantum computing techniques offer a new way to investigate these challenging systems: the quantum simulation approach. Combining current available noise intermediate-scale quantum (NISQ) devices with variational quantum eigensolver (VQE) algorithm to solve quantum many-body problems has attracted extensive attention. Although the NISQ devices have up to hundreds of qubits, treating a quantum many-body problem with a similar size on these devices is still impossible. One fundamental reason for this is the lack of scalability (i.e., the required quantum resources increase much faster than the increase of the problem size). In this presentation, I will introduce how to realize scalable VQE calculation in the symmetry-protected topological (SPT) phase [1] and the intrinsic topologically ordered phase [2] by designing problem-specified scalable parameterized quantum circuit (PQC) Ansatze. For the former, we construct a PQC with a two-layer structure to capture both the basic entanglement structure and finite correlations of an SPT Haldane phase in the non-exactly solvable alternating Heisenberg chain. For the latter, we construct a real-device-realizable PQC which can represent a weight-adjustable quantum loop gas to study the toric code model in an external magnetic field (also non-exactly solvable). In both cases, we obtain accurate ground states of the system with different sizes in the VQE simulation. [1] Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki, “Efficient variational quantum circuit structure for correlated topological phases” arXiv:2303.17187 (2023). [2] Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki, “Parameterized quantum circuit for weight-adjustable quantum loop gas” Phys. Rev. B 107, L041109 (2023)
- Shreya Vardhan (Stanford University)
- "Local dynamics and the structure of chaotic eigenstates"
[Abstract]
Abstract
We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We divide the system into two extensive subsystems, and study the relation between the energy eigenstates of the full system and products of energy eigenstates of the subsystems. The relation between these two bases can be used to understand dynamical properties of the system during thermalization, including the evolution of the Renyi entropies of a product of subsystem eigenstates. By studying a family of chaotic spin chains in (1+1) dimensions, we find that the magnitudes of the coefficients relating the two bases have a simple universal form as a function of $\omega$, the energy difference between the full system eigenstate and the product of eigenstates. This form differs from previous proposals of Lu and Grover, and Murthy and Sredniki. The phases of the coefficients show some surprising features. While it is generally expected that such phases are uncorrelated random variables, it turns out that there are significant correlations among them which do not have an analog in non-local chaotic systems. These correlations lead to a smaller value of the entanglement velocity than the one predicted by a random phase approximation. (Work in progress with Hong Liu and Zhengyan Darius Shi.)
- Yi Zhou (Institute of Physics, Chinese Academy of Sciences)
- "When Gutzwiller meets DMRG: a microscopic-wavefunction-guided approach to 2D correlated electrons"
[Abstract] [pdf]
Abstract
Two-dimensional (2D) strongly correlated electrons remains one of central themes in modern physics. In this talk, we address a crucial issue: whether there exists a paradigm to study 2D strongly correlated electrons, starting from its one-dimensional reduction? We will demonstrate that newly proposed Gutzwiller projected wavefunction guided density matrix renormalization group (DMRG) is a promising method on this theme. This novel method will be illustrated by two examples: (1) The benchmark on the famous Kitaev honeycomb model; (2) Attacking a challenging problem: what is the ground state of the antiferromagnetic Heisenberg model on a Kagome lattice?
- Takahiro Anan (Department of Applied Physics, The University of Tokyo)
- "Time-dependent Gutzwiller simulation of circularly polarized light-induced topological superconductivity"
[Abstract]
Abstract
Floquet theory enables us to map a time-periodic problem to an effective static one. The obtained effective static Hamiltonian turns out to realize novel quantum phases including topological insulators. In recent years, novel quantum phases are investigated with this theory, under the name of “Floquet engineering.” In a recent study [1], photo-induced topological superconductivity was theoretically proposed for the Hubbard model illuminated by circularly polarized light, with the use of the high-frequency expansion, which is a perturbative method valid for high-frequency driving. In this previous study, they take account of dynamical effects on the pairing interaction, by which they successfully incorporate the light-modulated strong-correlation effect into the superconducting gap function. However, since their prediction is limited to the high-frequency regime, a theoretical method valid even in low-frequency regime including infrared and THz regimes is desired from the experimental point of view. In this study, we adopt the time-dependent Gutzwiller approximation and directly compute the time evolution of the periodically-driven t-J model numerically, instead of performing the high-frequency expansion. In this presentation, I will explain this method and the numerical results of light-induced topological superconductivity.
[1]S. Kitamura & H. Aoki Commun. Phys. 5, 174 (2022)
- Takamasa Ando (Yukawa Institute for Theoretical Physics, Kyoto University)
- "Duality constructions of intrinsically gapless SPT models"
[Abstract]
Abstract
In this presentation, we present a general procedure for constructing intrinsically gapless SPT (igSPT) models in one spatial dimension. igSPT models have non-anomalous symmetries at the UV scale but exhibit 't Hooft anomalies in the IR regime. Our construction is based on gauging the symmetries. We explore different types of specific lattice models, including the fermionic Gu-Wen type anomaly.
- Leilee Chojnacki (Okinawa Insitute of Science and Technology)
- "Analogue gravitational waves in quantum magnets"
[Abstract] [pdf]
Abstract
Many extreme phenomena in our Universe, such as gravitational waves, are challenging to reproduce in laboratory settings. However, parallels with condensed matter systems can provide alternative routes for experimental accessibility. Here we show how spin nematics provide a low-energy avenue for accessing the physics of linearized gravity, in particular for the realization of gravitational wave-like, relativistically dispersing spin-2 excitations. We show at the level of the action that the low-energy effective field theory for a spin nematic is in correspondence with that of linearized gravity. We then explicitly identify a microscopic model of magnetism whose excitations in the low energy limit are relativistically dispersing, massless spin-2 bosons which are in one-to-one correspondence with gravitational waves, and outline a procedure for directly observing these analogue waves in a cold gas of $^{23}$Na atoms.
- Ippei Danshita (Department of Physics, Kindai University)
- "Quantum many-body scars of the Bose-Hubbard model with strong three-body losses"
[Abstract]
Abstract
Thanks to their recent observations in systems of Rydberg atoms in optical tweezer arrays and ultracold bosons in optical lattices, quantum many-body scar states (QMBSs) have attracted intensive interest in recent years. In this study, on the basis of the construction method of QMBSs for the spin-1 XY model, we find QMBSs of a restricted Bose-Hubbard model where the occupancy of more than two particles at a site is forbidden. Such a constraint can be realized by utilizing strong three-body losses near the Feshbach resonance. Using a modified Holstein-Primakoff expansion, we discuss the correspondence between the two models. We also propose how to experimentally prepare and probe the QMBSs with ultracold bosons in optical lattices.
- Mateo Olivier Jean-Marie Michel FONTAINE (KEIO University)
- "Phase diagram of a spin-1/2 XXZ ladder with a four-spin ring exchange"
[Abstract]
Abstract
We study the ground-state phase diagram of a spin-½ XXZ model with four-spin ring exchange on a two-leg ladder. The spin-chirality duality transformation allows us to relate the regimes of weak and strong four-spin interactions. By applying the Abelian bosonization and the duality, we analyze a simplified model in which part of the four-spin interactions is removed, and predict a phase diagram that contains distinct gapped featureless and ordered phases. In particular, we predict Neel and vector chiral orders in the presence of easy-axis anisotropy, and two distinct symmetry protected topological phases in the presence of easy-plane anisotropy. We performed numerical simulations for both the simplified and full models to confirm the predicted phase structure. We demonstrated that the two SPT phases and a trivial phase are distinguished by topological indices in the presence of certain symmetries.
- Shu Hamanaka (Kyoto University)
- "Skin effect in interacting systems"
[Abstract]
Abstract
Topology plays a crucial role in contemporary condensed matter physics, particularly concerning the emergence of novel phenomena resulting from strong correlations, such as topological Mott insulators and interaction-driven topological insulators [1,2]. Recent advancements have spurred active investigations into non-Hermitian topology [3], which arises due to the non-Hermiticity of systems and manifests as unique point-gap topology. Previous studies employing band theory have established that nontrivial point-gap topology leads to non-Hermitian skin effects, where the eigenvalues and eigenstates of the Hamiltonian exhibit significant dependence on boundary conditions [4]. While most research on non-Hermitian topology has focused on non-interacting systems, the ability to manipulate both dissipation and correlations in ultracold atoms has opened up avenues to explore the interaction effects on non-Hermitian topological systems [5]. In this study, we address whether strong interactions can induce non-Hermitian skin effects [6]. By analyzing a one-dimensional correlated model incorporating on-site two-body loss, we demonstrate that interactions can induce sensitivity to boundary conditions. Moreover, we verify the presence of nontrivial topological numbers.
[1] S. Raghu, et al., Phys. Rev. Lett. 100, 156401 (2008).
[2] M. F. Lapa, et al., Phys. Rev. B 93, 115131 (2016).
[3] Y. Ashida, et al., Adv. Phys. 69, 249 (2020).
[4] N. Okuma et al., Phys. Rev. Lett. 124, 086801 (2020).
[5] K. Sponselee, et al., Quantum Sci. Technol. 4, 014002 (2018).
[6] W. N. Faugno and T. Ozawa, Phys. Rev. Lett. 129, 180401 (2022).
- Kenji Harada (Graduate School of Informatics, Kyoto University)
- "Optimal network structure of quantum-inspired generative modeling"
[Abstract]
Abstract
Tensor networks (TN) have been widely and successfully used in physics. Since TN is an effective tool for representing a large composite tensor, such as quantum many-body states, new applications of TN for processing tensor data in other fields have been proposed. Here, we introduce a quantum-inspired generative modeling algorithm to create a parametric model for data distribution. It is called the Born machine. Although most applications of TNs fix the network structure as an ansatz, we tried to optimize the network structure of tree TNs, which represent a wave function of a ground state. We extend a similar idea to generative modeling. The new method performs better than the previous method using MPS and balance tree TNs, and can spontaneously produce the emergent structure for given data.
- Tomoya Hatanaka (The University of Tokyo)
- "Floquet code and the classification of topological phases"
[Abstract]
Abstract
Recently, a time-driven Floquet code [1] has been proposed, which does not have logical qubits when viewed as a system code, but has temporary logical qubits through periodic measurements, enabling error correction. Unlike toric code, which requires four qubits for measurement, Floquet code requires only two qubits, and is therefore attracting attention in terms of implementation of quantum computation. In addition, research on Floquet code and the classification of topological phases [2] has been conducted, attracting attention from the viewpoint of topological matter. In this presentation, we will present our study and research on the stability of topological phases and quantum circuit complexity with respect to the Floquet code.
[1] M. B. Hastings and J. Haah, Dynamically Generated Logical Qubits, Quantum 5, 564 (2021).
[2] D. Vu, A. Lavasani, J. Y. Lee, and M. P. A. Fisher, Measurement-Induced Floquet Enriched Topological Order, http://arxiv.org/abs/2303.01533.
- Toshiya Hikihara (Graduate School of Science and Technology, Gunma University)
- "Tree tensor network approaches for quantum many-body systems with quenched randomness"
[Abstract]
Abstract
My presentation concerns the applications of numerical approaches based on tree tensor networks (TTNs) to quantum many-body systems with quenched randomness. The approaches include the tensor-network strong-disorder renormalization group and a variational algorithm with TTN structural optimization. I will discuss how we can construct a TTN with an optimal network structure to represent the entanglement geometry of the target quantum state. The results of applying the methods to various systems will be reported.
- Yuya Ikeda (The University of Tokyo)
- "Photocurrent induced by a bicircular light drive in centrosymmetric systems"
[Abstract]
Abstract
A bicircular light (BCL) consists of two left-handed and right-handed circularly polarized lights with different frequencies, which draws a rose curve trajectory with a rotational symmetry determined by the ratio of the two frequencies. Recently, two-frequency drive such as the BCL drive has attracted an attention as a method to dynamically control the spatial symmetries including inversion symmetry, which cannot be controlled by a conventional monochromatic light drive [1-3]. Here we show that an application of a BCL to centrosymmetric or rotational symmetric systems allows a photocurrent generation through introduction of an effective polarity to the system [4]. The formula for the BCL-induced photocurrent is derived from the Feynman diagrammatic method and Floquet-Keldysh theory. We theoretically clarified that the direction of the photocurrent can be controlled by the relative phase of the two circularly polarized lights, where the relative phase serves a knob to rotate the rose pattern drawn by the BCL wave. The obtained formula is applied to the 1D SSH model and 3D Dirac/Weyl semimetals. In Dirac semimetals, we have found that a huge photocurrent is obtained due to its gapless nature. Moreover, nonperturbative effects on the photocurrent with the light intensity are also derived with Floquet-Keldysh formalism. It is shown that a saturation effect induces a crossover of the photocurrent dependence on the light intensity from J∝A^3.
[1] O. Neufeld et al., Nature Communications 10, 405 (2019).
[2] T. V. Trevisan et al., Phys. Rev. Lett. 128, 066602 (2022).
[3] Y. Ikeda, S. Kitamura, and T. Morimoto, Prog. Theor. Exp. Phys. 2022, 04A101 (2022).
[4] Y. Ikeda, S. Kitamura, and T. Morimoto, arXiv:2303.01796
- Junmo Jeon (Korea Advanced Institute of Science and Technology)
- "Localization control born of intertwined quasiperiodicity and non-Hermiticity"
[Abstract]
Abstract
Quasiperiodic systems are ordered without periodic length scale. Based on their incommensurate order, novel physical properties such as critical states have been activsly discussed. However, in open systems generally described by the non-Hermitian Hamiltonians, it is hardly known how such quasiperiodic order would lead to new phenomesa. In this work, we show that the intertwined quasiperiodicity and non-Hermiticity in terms of non-reciprocal hopping phase can give rise to striking effects: perfect delocalization of the critical and localized states, which is never allowed for Hermitian quasiperiodic systems. By using inverse participation ratio and the fractal dimension, we discuss the non-Hermitian hopping phase leads to delicate control of localization characteristics of the wave function. Our work offers (1) delocalization transition in quasiperiodic systems via non-Hermitian hopping phase, (2) experimental realization of controllable localized, critical and delocalized states, using photonic crystals.
- Bernhard Jobst (Technical University of Munich)
- "Finite-depth scaling of infinite quantum circuits for quantum critical points"
[Abstract]
Abstract
The scaling of the entanglement entropy at a quantum critical point allows us to extract universal properties of the state, e.g., the central charge of a conformal field theory. With the rapid improvement of noisy intermediate-scale quantum (NISQ) devices, these quantum computers present themselves as a powerful tool to study critical many-body systems. We use finite-depth quantum circuits suitable for NISQ devices as a variational ansatz to represent ground states of critical, infinite systems. We find universal finite-depth scaling relations for these circuits and verify them numerically at two different critical points, i.e., the critical Ising model with an additional symmetry-preserving term and the critical XXZ model.
- Hironori Kazuta (Department of Physics, Kindai University)
- "Quantum simulation of non-ergodic behavior in a disorder-free Bose-Hubbard system"
[Abstract]
Abstract
The recent development in cold-atom experiments has offered unique opportunities for studying non-equilibrium dynamics of isolated quantum systems. In order to understand how an isolated quantum system reaches thermal equilibrium through unitary time evolution, it is important to investigate mechanisms of nonergodic systems, such as integrability, many-body localization, quantum many-body scar states, and the Hilbert space fragmentation (HSF). In this work, following the protocol proposed by two of us, we analyze nonergodic dynamics due to HSF in a one-dimensional Bose-Hubbard system by means of a quantum simulator built with ultracold Bose gases in optical lattices. Specifically, we choose two different states as initial states. In the first (second) state, each odd-numbered site is singly (doubly) occupied, and each even-numbered site is empty. We show that in contrast to the case of the first state, the atomic density is not relaxed to equilibrium even after long-time evolution starting from the second state, exhibiting nonergodic behavior. In order to cross-check the quantum-simulation results, we numerically simulate the real-time evolution starting from each state with use of matrix product states.
- Nico Kirchner (Technical University of Munich)
- "Simulation of Anyonic Tight-Binding Hamiltonians"
[Abstract]
Abstract
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general abelian and non-abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for semions, Fibonacci anyons and Ising anyons. Additionally, we simulate non-equilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times - indicating thermalization.
- Masaya Kunimi (Tokyo University of Science)
- "Proposal for realizing quantum spin models with Dzyaloshinskii-Moriya interaction using Rydberg atoms"
[Abstract]
Abstract
We propose a method for realizing highly controllable quantum spin models with Dzyaloshinskii-Moriya interaction (DMI) in Rydberg atom quantum simulators. Our scheme is based on a two-photon Raman transition and transformation to the spin-rotating frame. The advantage of our scheme is that the ratio between the exchange interaction and DMI can be tuned in a wide range. We investigate the quantum dynamics of the Hamiltonian that includes only the DMI and magnetic field term, dubbed the DH model. We show that the dynamics are quite different from the classical case. We also find that the DH model has quantum many-body scar states (QMBS) and the nonergodic dynamics affected by the QMBS states.
- Hyeongmuk Lim (Center for Correlated Electron Systems, Seoul National University)
- "Real Hopf Insulator"
[Abstract]
Abstract
Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy invariant and the related band topology of three-dimensional (3D) real-valued Hamiltonians with two occupied and two unoccupied bands. Such a real Hamiltonian generally appears in $\mathcal{PT}$ symmetric spinless fermion systems where $\mathcal{P}$ and $\mathcal{T}$ indicate the inversion and time-reversal symmetries, respectively. We show that the 3D band topology of the system is characterized by two independent Hopf invariants when the lower-dimensional band topology is trivial. Thus, the corresponding 3D band insulator with nonzero Hopf invariants can be called a real Hopf insulator (RHI). In sharp contrast to all the other topological insulators discovered up to now, the topological invariants of RHI can be defined only when both the occupied and unoccupied states are simultaneously considered. Thus, the RHI belongs to the category of delicate topological insulators proposed recently. We show that finite-size systems with slab geometry support surface states with nonzero Chern numbers in a $\mathcal{PT}$-symmetric manner, and establish the bulk-boundary correspondence. We also discuss the bulk-boundary correspondence of rotation symmetric RHIs using the returning Thouless pump.
- Riku Masui (Yukawa Institute for Theoretical Physics, Kyoto University)
- "Robustness of Symmetry-Protected Topological Phases as a Resource of the Measurement-Based Quantum Computation"
[Abstract]
Abstract
The one-dimensional AKLT state is a typical example of symmetry-protected topological (SPT) phase. In one dimensional quantum system, SPT phases are differentiated from the trivial phase by the finite string order parameter (SOP) and even degeneracy of the entanglement spectra. It is known that SPT phases have short range entanglement, which can be applied to measurement-based quantum computation (MBQC). This motivates us to use the gate fidelity [1] as a new order parameter of SPT phase and to study the stability of SPT phase in the open quantum system, so this enables us to study the stability of SPT phase in from the quantum-computational point of view. In [2], symmetries of quantum channels which can or cannot keep the SPT order are discussed with their calculation of string order parameter. According to their results, the dephasing noise can keep the SPT order of Haldane phase, but the depolarizing noise destroys that. So, we numerically calculated the gate fidelity of Z-rotation gate realized by the MBQC on the AKLT state decohered by the two noises. We show that the behavior of gate fidelity against two kinds of noise is consistent with the result of [2], and moreover we propose the gate fidelity as a new order parameter because gate fidelity more clearly shows the difference between two noises than string order parameter. We also show the numerical results of gate fidelity and string order parameter of the AKLT state at the finite temperature, and discuss the relation between the gate fidelity and string order parameter.
- Shohei Miyakoshi (Center for Quantum Information and Quantum Biology, Osaka University)
- "The effect of diamond-type shaped multi-qubit decomposition for one-dimensional quantum state dynamics"
[Abstract]
Abstract
Quantum computing has been a hot topic in recent years, with many algorithms being developed to construct quantum circuits for many-body states. However, the construction methods for highly-entangled quantum states are still under development and require further refinement. In this paper, we focus on the reproducibility of many-body states using a quantum circuit consisting of multi-qubit gates. We also examine the efficiency of a quantum circuit constructed by two-qubit gates in quench dynamics for the transverse-field Ising model. This model undergoes long-time evolution and can result in highly-entangled quantum states. Our results demonstrate that a diamond-shaped quantum circuit approximating the multi-qubit circuit can efficiently reproduce the long-time dynamics. Additionally, we find that the diamond-type circuit reflects the volume law in entanglement entropy, providing an advantage over other circuit shapes.
- Yuki Miyazaki (Aoyama Gakuin University)
- "Evaluation of Quantum Entanglement via Permutationally Invariant Quantum State Tomography"
[Abstract]
Abstract
Quantum state tomography (QST), in which the density matrix of a quantum many-body system is reconstructed by the expectation values of a set of observables, is experimentally hard due to (i) the exponential increase of degrees of freedom with system size and in the case of cold atomic systems in optical lattice, (ii) the practical problem of local quantization axis rotation. In a previous work [G. Tóth et al., PRL 105, 250403 (2010)], permutationally invariant (PI) QST was introduced as the reconstruction of the part of a density matrix that is invariant under permutations of lattice sites. It has been reported not only that PIQST can avoid the above issues [(i) and (ii)], but also that the PI part of a density matrix can encode some important properties of the original density matrix [T. Gao et al., PRL 112,180501 (2014)]. In this work, we investigate the relation between the PI part of a density matrix and some entanglement measures and propose an efficient method to evaluate quantum entanglement via PIQST with Monte Carlo algorithm.
- Kanto Miyazako (The Open University of Japan)
- "Effect of particle number conservation law on Family-Vicsek scaling in one-dimensional quantum systems."
[Abstract]
Abstract
In surface-roughness growth of classical systems, scaling invariance often emerges, which is called Family-Vicsek (FV) scaling. Recently, the emergence of the FV scaling was numerically found in fluctuations of the local particle number in one-dimensional quantum systems. However, it is unclear what factors are essential for the appearance of the FV scaling in quantum systems. We study several quantum lattice models, such as the transverse-field Ising model and BCS-like quadratic fermion model, in which the breaking of the particle number conservation law can be controlled by changing model parameters, and discuss the relationship between the particle number conservation law and the FV scaling.
- Yusuke Nakai (Yukawa Institute for Theoretical Physics, Kyoto University)
- "Topological enhancement of non-normality in non-Hermitian skin effects"
[Abstract]
Abstract
The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.
- Koutaro Nakajima (Graduate School of Science and Technology, Niigata University)
- "Simulation of the angular-time evolution on AKLT chain using IBM quantum computer"
[Abstract]
Abstract
In our previous work, we revealed that in the AKLT chain the parameter-time evolution by entanglement Hamiltonian, which is spin precession, can capture the information of the entanglement. In this poster presentation, we verify whether this phenomenon actually works using IBM quantum computer.
- Shunsuke Nishimura (Department of Physics, The University of Tokyo)
- "Asymmetric spin transport in the U(1)-symmetric random unitary circuits with quantum feedback controls"
[Abstract]
Abstract
Random unitary circuits (RUCs) and their measurement-induced phase transitions have been intensively investigated [1]. However, the dynamics in the presence of both quantum measurements and quantum feedback control is less examined [2]. We have studied the real-time dynamics of the U(1)-symmetric RUC with composite operators consisting of a local projective measurement onto two adjacent sites and a spin-flip operator depending on the measurement outcome. In our simulation, we find the asymmetric spin transport in the U(1)-symmetric RUC as the effect of quantum feedback control. Moreover, we explore the relationship between the feedback occurrence rate and the time dependence of the polarization of the U(1) charge.
[1] M. P. A. Fisher, V. Khemani, A. Nahum, and S. Vijay, Annal. Rev. of Condens. Matter Phys., 14:1, 335-379 (2023).
[2] V. Ravindranath, Y. Han, Z.-C. Yang, and X. Chen, Entanglement Steering in Adaptive Circuits with Feedback, arXiv:2211.05162 (2022).
- Shuhei Ohyama (Yukawa Institute for Theoretical Physics, Kyoto University)
- "Higher structures in matrix product states"
[Abstract]
Abstract
The Berry phase, introduced by Michael V. Berry in 1984, has been widely applied in the definition of topological invariants, inspired by the trend of topological phases originating from quantum Hall systems. However, when naively calculating the Berry phase for high-dimensional many-body Hamiltonians, a divergence problem arises in the thermodynamic limit, necessitating an appropriate generalization of the definition of the Berry phase. In this presentation, I will discuss the formulation of higher Berry phases in one-dimensional systems, based on [2]. Specifically, by employing the matrix product state, we define the inner product for three states and demonstrate how this quantity provides a natural definition of the higher Berry phase.
[1] Shuhei Ohyama, Yuji Terashima, Ken Shiozaki arXiv:2303.04252.
[2] Shuhei Ohyama, Shinsei Ryu arXiv:2304.05356.
[3] Ken Shiozaki, Niclas Heinsdorf, Shuhei Ohyama, arXiv:2305.08109.
- Jonathan Oppenheim (University College London)
- "Path integrals for hybrid quantum classical systems"
- Hisanori Oshima (Applied physics, The University of Tokyo)
- "Entanglement and charge-fluctuation in U(1) symmetric Clifford unitary circuit games"
[Abstract]
Abstract
In unitary circuit games, a quantum pure state evolved by scrambling local unitary gates is subject to stochastic local unitary "disentangler" actions. It has recently been found that the entanglement entropy in such a system undergoes a phase transition from a volume-law phase to an area-law phase. In this presentation, we numerically study transitions in a U(1) symmetric Clifford unitary circuit game. In addition to the entanglement transition, we discover a charge-fluctuation transition that can be characterized by a correlation function of U(1) charges. Although both of these transitions have been previously studied in the context of measurement-induced transitions under U(1) symmetry, whether these transitions are distinct or not remains to be concluded. In our system, these transitions appear at distance in the parameter space and can be clearly distinguished.
- Soshun Ozaki (The University of Tokyo)
- "Dynamics of the Clean Sachdev-Ye-Kitaev model"
[Abstract]
Abstract
The Sachdev-Ye-Kitaev (SYK) model [1,2] consists of Majorana fermions with random all-to-all interactions, which is maximally chaotic in the sense that the Lyapunov exponent of the model saturates the Maldacena-Shenker-Stanford bound [3]. Its relevance to the physics of black holes is also well discussed. To elucidate the importance of the randomness in the characteristic dynamics of the SYK model, we investigate the SYK model without the disorder, the clean SYK model. This model turns out to be solvable and allows us to compute the dynamical quantities for a large number of Majorana fermions. In our presentation, we first derive the eigenenergies and corresponding eigenstates. Using the obtained eigenstates and eigenenergies, we evaluate the thermodynamic and dynamical properties of the four-body clean SYK model, the level-spacing statistics, entropy, spectral form factor (SFF), and out-of-time-order correlators (OTOCs). In particular, the SFF and OTOCs are considered to characterize quantum chaos. Our analytical and numerical results show that the SFF is not chaotic, but the OTOC has a signature of scrambling. The differences in these quantities between the clean SYK model and the original one will be discussed.
[1] A. Kitaev, A Simple Model of Quantum Holography, KITP Program: Entanglement in Strongly-Correlated Quantum Matter, Santa Barbara, 2015, http://online.kitp.ucsb.edu/online/entangled15/.
[2] K. Jensen, Phys. Rev. Lett. 117, 111601 (2016).
[3] J. Maldecena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08, 106 (2016).
- Tanay Pathak (Indian Institute of Science)
- "Krylov complexity and saddle dominated scrambling"
[Abstract]
Abstract
In this presentation I will discuss about certain systems which are integrable but shows similar features that of chaotic systems due to the presence of the unstable saddle points. Furthermore, I will present the study of the behaviour of Krylov complexity in such systems.
- Baishali Roy (Ramakrishna Mission Vivekananda Educational and Research Institute, Belur)
- "Chaos in periodically driven CFTs and their bulk dual"
[Abstract] [pdf]
Abstract
Out-Of-Time-Ordered-Correlation functions (OTOCs) in thermal equilibrium have been used as a diagnostic of chaos in QFTs for times much smaller than the "scrambling time". I will mainly present our recent papers (JHEP 08 (2022) 221, arXiv:2212.04201), which show that the OTOCs continue to be a good diagnostic of chaos even when the system is out of equilibrium. As an explicit example, we study OTOC's in a class of periodically driven CFTs. The drive profile breaks time and spatial translational symmetry. Due to the lack of translational invariance, the OTOCs show some novel features, such as a spatially dependent "butterfly velocity". We have compared the behaviour of the OTOCs with the case of the "un-driven thermal CFT". We show that even in this non-equilibrium example, the OTOCs continue to demarcate chaotic and integrable CFTs. Additionally, I will present our recent progress in constructing the dual bulk metrics corresponding to the different phases of a discretely driven CFT, where a probe bulk brane can detect a first order phase transition between two phases. We also compare the bulk and boundary results by computing correlators in the bulk.
- Dita P. Sari (Shibaura Institute of Technology)
- "muSR study of hole-doped organic strange metals kappa-(ET)4Hg3-dX8; X=Br, Cl"
[Abstract] [pdf]
Abstract
The hole-doped organic metal kappa-(ET)4Hg3-dBr8, d=11% (k-HgBr) and kappa-(ET)4Hg3-dCl8, d=22% (k-HgCl), where ET = (CH2)2S8C6S8(CH2)2, are exceptional carrier-doped metal among half-filled organics, beside ET dimer tend to arrange triangular lattice. k-HgBr undergoes superconductor while k-ET-HgCl transitions to the insulator at ambient pressure and becomes superconductor under pressure. k-HgBr is discussed as a doped quantum spin liquid metal because, although it is superconductor at ambient pressure the magnetic susceptibility behavior is well scaled to that of organic spin-liquid insulator, k-(ET)2Cu2(CN)3. Further, k-HgBr shows non-Fermi liquid (NFL) behavior evidenced by linear temperature dependence of resistivity, supported by NMR and muon spin rotation (muSR) spectroscopies. The specific heat studies showed both compounds have a large residual heat capacity and close to quantum critical point (QCP). On the other hand, the recent developing study on SYK model demonstrate the phase diagram not only of spin-1/2 fermion with QCP and spin liquid (Kim-group and Sachdev group), but also of the holographic superconductor in the QCP with NFL-FL crossover (Schmalian-group). Here we characterize superconductivity and spin dynamics, leading to the degree of quantum entanglement, in k-HgBr and k-HgCl, using comprehensive muSR measurements and are proposing that both compounds are a good platform to study SYK model.
- Tokuro Shimokawa (Okinawa Institute of Science and Technology)
- "Entanglement-Based Detection of Quantum Frustrated Random Singlet State in Spin Liquid Candidates"
[Abstract]
Abstract
The possible realization of a novel state called the quantum frustrated random singlet (QFRS) state has been reported in several quantum frustrated Heisenberg model with bond randomness. This state exhibits qualitatively different behavior, such as the presence of quasi orphan spins, from the one-dimensional quantum random singlet state that occurs in the absence of frustration. One of the reasons why this state has attracted attention is that the spin-liquid-like behaviors observed in some candidate materials for quantum spin liquids (QSLs) may be understood as the behaviors of this QFRS state. However, there has been a strong demand for a solution to the problem of how to distinguish between the QSL state and the QFRS state in experiments. To tackle this problem, we propose using entanglement measures to distinguish between these states. Specifically, we focus on several entanglement monotones, including one-tangle and two-tangle, which can be witnessed through inelastic neutron scattering experiments. We apply these ntanglement measures to the S=1/2 random-bond triangular-lattice Heisenberg antiferromagnet to investigate the entanglement properties of the QFRS state in the context of exact-diagonalization and calculation based on quantum-typicality. The most important remark is that the finitetemperature dependence of the two-tangle can distinguish between the QFRS and some QSL states, such as those that emerge in the S=1/2 J1-J2 triangular-lattice and Kagome Heisenberg antiferromagnets. Our results demonstrate that these entanglement measures are powerful tools for detecting the QFRS state in some QSL candidates, thereby solving the long-standing identification problem in experiments.
- Kenji Shimomura (Yukawa Institute for Theoretical Physics, Kyoto University)
- "The absence of the non-Hermitian skin effect in Hermitian systems and Fock space skin effect"
[Abstract]
Abstract
We propose a formulation of the non-Hermitian skin effect (NHSE) in free systems only using some eigenstates, applicable to one- or higher-dimensional systems and even the generic geometry systems. Furthermore, we extend it to many-body systems and introduce the NHSE in the many-body Fock space (dobbed ``Fock space skin effect''), discussing the relation with the Liouvillian skin effect, slowing down of relaxation in dissipative systems. For this purpose, we define ``localization'' and ``localization length'' of state vectors in our manner. We rigorously show that if the number of given state vectors localized at the same location exceeds a certain threshold, a Hamiltonian such that all of their state vectors are right eigenstates of it must be non-Hermitian. If the NHSE is characterized by the fact that more states than the threshold are localized at the same location, then we can conclude that the NHSE in this sense cannot occur in Hermitian systems.
- Takafumi Suzuki (University of Hyogo)
- "Ground states of an extended honeycomb-lattice Kitaev-\Gamma model"
[Abstract]
Abstract
We have investigated the ground-state phase diagram of an extended Kitaev-\Gamma model on a honeycomb lattice by means of exact diagonalization and densitry-matrix renormalization group. In this study, we start from isolated Kitaev-\Gamma spin chains and add an interchain coupling between the spin chains. By increasing the interchain coupling, the model becomes the isotropically-interacting Kitaev-\Gamma model on a honeycomb lattice. We find that the obtained ground-state phase diagram includes interesting points in addition to the findings reported in arXiv:2212.11000. For instance, in the spin-chain limit, a valence bond solid phase appears when the \Gamma interaction is weak. In addition, the characteristics of some magnetically ordered phases are explained by a six-site transformation independently of the strength of the interchain interactions.
- Hung-Hsuan Teh (The Institute of Solid State Physics, The University of Tokyo)
- "Chiral Gauge Fields in Laser Irradiated 3D Dirac Semimetals"
[Abstract]
Abstract
Floquet engineering has become a powerful tool for investigating laser-induced coherent phenomena in quantum materials. In this talk, we focus on a 3D Dirac semimetal irradiated by a circularly polarized laser field which leads to an effective chiral gauge field. Under such irradiation, a Floquet Weyl pair and corresponding Fermi arc states emerge. By further taking into account the skin effect from the semimetal surface, a chiral gauge field with space dependence leads to nonzero chiral magnetic field. In this setup, one of the originally localized Fermi arc states leaks into the bulk and transforms into a delocalized chiral Landau level state. By introducing a homogeneous impurity, a net chiral current can be achieved due to the disparity between these two chiral states. Alternatively, the real space distinction can generate temperature and chemical potential gradients, thereby also resulting in a chiral current. The findings of our study provide a foundation for exploring various anomalies in quantum materials.
- Hiromu Ushihara (Department of Physics, The University of Tokyo)
- "Derivation of the quantum master equation for the Fermi–Hubbard model with two-body losses"
[Abstract]
Abstract
An open quantum system, a system coupled to external baths, can serve as a platform for studying non-equilibrium phenomena. The Hubbard model with two-body losses is a prototypical model of open quantum many-body systems, which has been widely studied both theoretically and experimentally. However, in previous studies, a quantum master equation describing the system has been phenomenologically introduced without microscopic derivation. In this study, we give a microscopic derivation of a quantum master equation for the Fermi–Hubbard model with two-body losses.
- Kazuya Yamashita (Department of Physics, Kyoto University)
- "Production of degenerate Fermi gases of lithium towards experiments on quantum information dynamics in optical lattices"
[Abstract]
Abstract
Recently, there has been a growing interest in quantum information-based approaches to quantum many-body and quantum non-equilibrium phenomena. In order to access this topic experimentally, we have been constructing a new device for producing degenerate gas of lithium combining high-resolution optical systems for measuring entanglement entropy in two-dimensional optical lattices. In presentation, we will report on the current status of the experiment.