Recently, noncoplanar spin configurations with nonzero spin scalar chirality have drawn considerable attention as an origin of the anomalous Hall effect. As a typical example, a scalar chiral state with noncoplanar four-sublattice magnetic ordering was theoretically proposed in a Kondo lattice model on a triangular lattice at 1/4 and 3/4 fillings [1-3]. The chiral states are both Chern insulators showing a quantization of the Hall conductivity. In the previous studies, however, localized moments are approximated as classical spins. It is interesting to ask how quantum spin fluctuations affect the nontrivial chiral order and electronic state of the system. Here, we examine the effect of quantum fluctuations by the linear spin-wave analysis with introducing the Holstein-Primakoff transformation to the localized spins. As a result, we find that the four-sublattice chiral order at 3/4 filling is fragile against quantum fluctuations within the present approximation, whereas it remains robust at 1/4 filling. We also find that the reduction of magnetic moment in the chiral phase is considerably small compared to those in typical antiferromagnetic phases in localized spin systems without itinerant electrons . In addition, by extending the analysis, we examine magnon transport properties. We find that, similar to a localized spin model , the Chern insulating phases in the present spin-charge coupled model exhibits a magnon Hall effect .
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We present a simple example of topologically trivial phases, in the sense that both phases are adiabatically connected to direct products of local states, only distinguished under site-centered inversion symmetry in one dimension. Existence of such phases is proven by an effective field theory using Abelian bosonization and a general argument based on the matrix-product state representation. We also provide a simple spin chain model which exhibits those phases and numerical results.
The pyrochlore material Tb\(_2\)Ti\(_2\)O\(_7\) has been the focus of intensive research as it does not show any conventional long-range order down to 50mK, and remains in a dynamic spin-liquid state. Recent experiments observed signatures of a (1/2,1/2,1/2) order in both neutron scattering and specific heat measurements [1-3]. We derive an effective pseudospin-1/2 Hamiltonian for Tb\(_2\)Ti\(_2\)O\(_7\) by projecting a microscopic Hamiltonian with the f-p hybridization to the lowest crystal field doublets [4,5]. We present a mean-field phase diagram of this Hamiltonian, and estimate the possible parameters in the spin Hamiltonian that give rise to the (1/2,1/2,1/2) in the real material.
[1 ] K. Fritsch, K. A. Ross, Y. Qiu, J. R. D. Copley, T. Guidi, R. I. Bewley, H. A. Dabkowska, B. D. Gaulin, Phys. Rev. B, 87, 094410 (2013)
[2 ] K. Fritsch, E. Kermarrec, K. A. Ross, Y. Qiu, J. R. D. Copley, D. Pomaranski, J. B. Kycia, H. A. Dabkowska, and B. D. Gaulin, arXiv:1312.0847
[3 ] T. Taniguchi, H. Kadowaki, H. Takatsu, B. Føak, J. Ollivier, T. Yamazaki, T. J. Sato, H. Yoshizawa, Y. Shimura, T. Sakakibara, T. Hong, K. Goto, L. R. Yaraskavitch, J. B. Kycia, Phys. Rev. 87, 060408(R) (2013)
[4 ] Shigeki Onoda and Yoichi Tanaka, Phys. Rev. B, 83, 094411 (2011)
[5 ] Hamid R. Molavian, Michel J.P. Gingras, and Benjamin Canals, Phys. Rev. Lett., 98, 157204 (2007)
SU(N) symmetric Heisenberg models may arise in different contexts in correlated insulators.The simplest example is the usual SU(2) Heisenberg model of a magnetic Mott insulating. When in addition, orbital degrees of freedom are also present, the relevant effective model is the spin-orbital Kugel-Khomskii model, which in its most symmetric form is identical to SU(4) Heisenberg model. The S=1 spin systems with bilinear S·S and biquadratic (S·S)\(^2\) interactions are SU(3) symmetric for special values of the coupling constants. For ultra-cold alkaline earth atoms trapped in optical lattices the nuclear spin F is the only relevant degree of freedom, with N=2F+1 possible states, which can lead to an SU(N) symmetric model as well.
We studied the ground state properties of the SU(3), SU(4) and SU(6) symmetric Heisenberg-model on the honeycomb lattice by several numerical methods: iPEPS tensor network algorithm, exact diagonalization, linear flavor wave theory and variatonal Monte Carlo calculations on Gutzwiller projected free-fermionic Fermi-sea states. Our findings for the SU(4) case show an algebraic spin-liquid phase, while plaquette ordered phases appear for the SU(3) and SU(6) cases. In the SU(6) case bond-meanfield approximation [Szirmai et al., PRA 84, 011611] prefers a chiral state, which in our calculations has comparable - but slightly higher - energy to the plaquette ordered phase. Introducing weak, ferro- or antiferromagnetic ring exchange interaction around the hexagonal plaquettes selects the chiral or the plaquette ordered phase, respectively.
[I] P. Corboz, M. Lajkó, A. M. Läuchli, K. Penc, F. Mila: Phys. Rev. X 2, 041013 (2012)
[II] P. Corboz, M. Lajkó, K. Penc, F. Mila, A. Lauchli, Phys. Rev. B 87, 195113 (2013)
[III] M. Lajkó, K. Penc, Phys. Rev. B 87, 224428 (2013)
A microscopic theory of the thermal response of the topological superconductors will be given. The theory is derived from the Majorana fermion coupled with the gravitational field, which effectively represents excitations of superconductors under a temperature gradient or those in a rotating system. We focus on temperature dependence of the thermal Hall coefficient of the two-dimensional topological superconductors.
We present a numerical simulation result of the spin-motive force with antiferromagnetic spin correlation using the time-dependent Schrodinger equation. We propose the formulation of the spin-motive force with antiferromagnetic spin correlation from the calculation result. In this research, we calculated time evolution of a conduction electron with ferromagnetic spin correlation and antiferromagnetic spin correlation in the one-dimensional system.In case of the antiferromagnetic correlation, the spin-motive force changes its direction from site to site, so the naive expectation is that net spin-motive force is not created for the conduction electron. However, we show that the spin-motive force acts on the conduction electron in the antiferromagnetic spin correlation case. The mechanism of the spin-motive force creation in antiferromagnetic case is clearly understood by making use of the unitary transformation. This simulation can be extended to various spin correlation case.
The spin-nematic phase and the 120-antiferromagnetic-ordered phase are expected in some parameter region in the spin-1 bilinear-biquadratic model on the triangular lattice, where the quantum-phase-transition point of these two phase has the SU(3) symmetry. We study the properties of topological defects on the SU(3) point in this model. First, we classify the defects by the homotopy theory, and study the energy and the dynamics of those. In addition.
Recent studies have reported the discovery of novel topological phases, which cannot be characterized by local order parameters but by the entanglement spectrum. We analyze the one dimensional cluster Ising model to show the robustness of the topological phase against random interactions. We calculate the entanglement spectrum and string order parameters using exact diagonalization. We find successive changes in degeneracy of the entanglement spectrum as we increase the degree of the randomness, which suggests the changes of symmetry.
Recently, SU(N) fermionic systems using alkaline-earth atoms in optical lattice was realized. Since novel quantum phases are expected to emerge, theoretical classification of quantum phases in SU(N) fermionic systems is important. We focus on the Mott phases in one dimension where one trivial and N-1 nontrivial topological classes exist. To identify the topological class, we develop how to construct order parameters for arbitrary even N. To check the validity of the order parameters, we study the system in one-dimensional two orbital SU(4) case using infinite Time Evolving Block Decimation (iTEBD). As a result, the topological class can be identified using the order parameters. This result is consistent with the fact obtained by the structure of low-lying entanglement spectrum.