## Gravitation and cosmology: principles and applications based on quantum information (21H05189)

General Relativity proposed by A. Einstein is the most convincing classical theory of gravity describing the dynamical fluctuations of space and time. Cosmological models based on General Relativity have successfully explained a bunch of phenomena observed in the Universe. Nevertheless, some fundamental issues remain long-standing puzzles. Of most prominence is the origin of the two phases of the accelerated expansion of the early and late universe, a.k.a. inflation and dark energy. This exposes a lack of our profound understanding of gravity and spacetime. In this project, we therefore aim to clarify the whole consistent picture of gravity and spacetime, which would make progress toward resolution of the beginning and the accelerated expansion of the Universe.

The research proposal of our group (C3) is two-fold: one is to incorporate the aspects of quantum information—which has been substantially developed during the past decade by the Ryu-Takayanagi formula in the gauge/gravity correspondence—into “braneworld.” A braneworld describes our 4-dimensional universe as a thin membrane corresponding to the boundary of higher dimensional anti-de Sitter spacetime. This model has been motivated by and consistently derived from particle physics. We try to reframe the braneworld model from the perspective of quantum information theory. It is our hope that this new braneworld perspective would be a powerful tool and provide a clue to get deeper insight into problems of universe.

Another blueprint of our research proposals is to identify the direct signature of quantum gravity by exploring a broad range of topics on gravitational physics. The recent experimental activities including the detection of gravitational wave signals and the image of supermassive black holes have reached a sensitivity where the deviation from General Relativity is testable. Stimulated by this new exciting window of opportunity in cosmology/astrophysics, we address phenomena that lead to the robust predictions of quantum aspects of gravity.

### Members in C03

**[Principal Investigator]**

Tetsuya Shiromizu Graduate School of Mathematics, Nagoya University

**[Co-Investigator]**

Keisuke Izumi Kobayashi-Maskawa Institute, Nagoya University

Tsutomu Kobayashi Department of Physics, Rikkyo University

Masato Nozawa Faculty of Engineering, Osaka Institute of Technology

Norihiro Tanahashi Faculty of Science and Engineering, Chuo University

Hirotaka Yoshino Graduate School of Science, Osaka Metropolitan University

**[ExU Postdoctoral Fellows(Research Collaborators)]
**Daisuke Yoshida Graduate School of Mathematics, Nagoya University

Norichika Sago Kyoto University / Osaka Metropolitan University

**[Research Collaborators]**

Sumio Yamada Faculty of Science, Gakushuin University

**[Graduate Students]**

Diego Soligon Graduate School of Mathematics, Nagoya University

Takamasa Kanai Graduate School of Mathematics, Nagoya University

Lee Kangjae Graduate School of Mathematics, Nagoya University

Lei Fu Graduate School of Mathematics, Nagoya University

Masaya Amo Yukawa Institute for Theoretical Physics, Kyoto University

Kensuke Sueto Graduate School of Science, Osaka Metropolitan University

## Tensor Networks and Quantum Many-Body Systems from Quantum Information (21H05191)

Quantum many-body systems such as quantum spin systems, ultra-cold atoms, and topological quantum matter, have been a central issue in modern condensed matter physics. The key to understanding such complex systems is the structure of quantum entanglement. The primary goal of group D02 is to precisely understand the physics of quantum many-body systems based on a quantitative analysis of quantum entanglement. For this purpose, we focus on tensor networks (TNs) that provide very practical numerical and theoretical frameworks for describing and controlling entangled many-body states. Recent years have witnessed a growing interest in applying TNs to various fields, ranging from quantum information to high-energy physics. In particular, the fusion of different fields has led to nontrivial results such as the relation between the Ryu-Takayanagi formula and the entanglement renormalization group, one of the TN methods. In this research project, motivated by such interesting interdisciplinary developments, we will systematically clarify the controlling mechanism of quantum many-body states using TNs, and then develop a modern theory of quantum many-body dynamics by focusing on mathematical structures behind the TNs and quantum entanglement. Also, we will address TN algorithms for higher dimensions and critical systems. In cooperation with other research groups, moreover, we explore condensed matter analogies of quantum gravity phenomena in realistic experimental situations, which would provide a possible understanding of quantum universe from the condensed matter perspective.

### Members in D02

**[Principal Investigator]**

Kouichi Okunishi Department of Physics, Niigata University

**[Co-Investigator]**

Kenji Harada Graduate School of Informatics, Kyoto University

Chisa Hotta Graduate School of Arts and Sciences, The University of Tokyo

Hosho Katsura Graduate School of Science, The University of Tokyo

Hiroshi Ueda Center for Quantum Information and Quantum Biology, Osaka University

**[ExU Postdoctoral Fellows(Research Collaborators)]**

Shunsuke Furuya, Graduate School of Arts and Sciences, The University of Tokyo

Atis Yosprakob Department of Physics, Niigata University

**[Research Collaborators]**

Toshiya Hikihara, Faculty of Science and Technology, Gunma University

Tomotoshi Nishino, Department of Physics, Kobe University

Tsuyoshi Okubo, Graduate School of Science, The University of Tokyo

**[Graduate Students]**

Atsushi Iwaki, Graduate School of Arts and Sciences, The University of Tokyo

Koutaro Nakajima, Graduate School of Natural Science, Niigata University

## Quantum Black Holes from Quantum Information (21H05184)

Black Holes are probably the most mysterious and interesting objects in the universe. Classically due to their strong gravitational forces, once you enter through the black hole horizon, you can never go out. However if one considers the quantum effects, this is not true anymore. In fact a black hole has definite temperature and radiates thermally (which is so-called Hawking radiation). Furthermore, a black hole has huge entropy, suggesting that a black hole is in fact a coarse-grained description of degenerate states, whose degeneracy is given by exponential of the entropy, according to the Boltzmann’s entropy formula. These suggest that one should also have a fine-grained description of gravity, which is quantum gravity and string theory is the most successful candidate for it. Recent studies show that two important concepts play an important role in understanding quantum gravity/string theory. One is quantum information. The other is gauge/string duality, which claims that certain quantum gravity is equivalent to certain gauge theory. Our main research goal is using these two important concepts, to understand the physics behind the horizon of quantum black holes, and how quantum mechanics is consistent with gravity. More concretely we would like to figure out the answer for the following key questions; how the physical information of the black hole leaks out through the Hawking radiation? How quantum gravity corrects Hawking’s mistake? What are the laws of physics behind the black hole horizon? Through the study of quantum black holes, we would like to understand the basic principles for quantum gravity.

### Members in B01

**[Principal Investigator]**

Norihiro Iizuka Department of Physics, Osaka University

**[Co-Investigator]**

Toshifumi Noumi Department of Physics, Kobe University

Masaki Shigemori Department of Physics, Nagoya University

Seiji Terashima Yukawa Institute for Theoretical Physics, Kyoto University

Tomonori Ugajin The Hakubi Center for Advanced Research, Kyoto University

**[ExU Postdoctoral Fellows(Research Collaborators)]
**Sunil Kumar Sake Department of Physics, Osaka University

Nicolò Zenoni Department of Physics, Osaka University

**[Research Collaborators]**

Kotaro Tamaoka College of Humanities and Sciences Department of Physics, Nihon University

Koji Hashimoto Department of Physics, Kyoto University

Kengo Maeda Faculty of Engineering, Shibaura Institute of Technology

**[Graduate Students]**

Takanori Anegawa Department of Physics, Osaka University

## Quantum information theoretic approach to the dynamics of quantum field theory (21H05190)

Many of the phenomena around us, such as the Standard Model of elementary particles, are described in terms of quantum field theory. Understanding the physics of the microscopic realm is important not only for investigating the ultimate constituents of matter, but also for exploring the nature of quantum many-body systems, in which many fundamental quantum systems cooperate with each other to create new physical phenomena. The goal of group D01 is to elucidate the dynamics of matter that exhibits such quantum behavior. In quantum information theory, how quantum systems change under various physical manipulations is investigated from a general viewpoint. By adopting the perspective of quantum information theory, new aspects of quantum field theory may be revealed that cannot be understood by conventional methods. In particular, by focusing on the common mathematical structure behind quantum field theory and quantum information theory, we hope to uncover universal properties that all field quantum theories should possess, independent of individual quantum systems. As a complementary approach to examining the dynamics of quantum field theories, we will perform quantum computer simulations of quantum field theories. Many physical systems, including finite density systems and real time systems, are difficult to simulate on classical computers, but are expected to be efficiently simulated on quantum computers. By developing and implementing methods of quantum computation suitable for quantum field theory, we will be able to elucidate important phenomena such as the scattering process of elementary particles and the evaporation process of black holes. Furthermore, we will explore the relationship between the quantum information theory aspect of quantum field theory and holographic principles as well as quantum gravity theory.

### Members in D01

**[Principal Investigator]**

Tatsuma Nishioka Department of Physics, Osaka university

**[Co-Investigator]**

Masazumi Honda Yukawa Institute for Theoretical Physics, Kyoto University

Etsuko Itou iTHEMS, RIKEN

Yutaka Matsuo Department of Physics, The University of Tokyo

Takuya Okuda Graduate School of Arts and Sciences, The University of Tokyo

**[ExU Postdoctoral Fellows(Research Collaborators)]
**Pratik Nandy Yukawa Institute for Theoretical Physics, Kyoto University

Dongsheng Ge Department of Physics, Osaka university

**[Research Collaborators]**

Takahiro Doi Research Center for Nuclear Physics, Osaka University

Kazunobu Maruyoshi Faculty of Science and Technology, General Education, Seikei University

Lento Nagano International Center for Elementary Particle Physics, The University of Tokyo

Ryo Suzuki Shing Tung Yau Center of Southeast University

Hiroyuki Tajima Department of Physics, The University of Tokyo

Shouichiro Tsutsui iTHEMS, RIKEN

Masahito Yamazaki Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo

Yutaka Yoshida Faculty of Law, Meiji Gakuin University

Daisuke Inotani The Research and Education Center for Natural Sciences, Keio University

Akira Matsumoto iTHEMS, RIKEN

Naohisa Sueishi Keio University

**[Graduate Students]**

Hiroki Sukeno Stony Book University

Yoshitaka Okuyama Department of Physics, The University of Tokyo

Kohki Kawabata Department of Physics, The University of Tokyo

Shinichiro Yahagi Department of Physics, The University of Tokyo

Taichi Nakanishi Yukawa Institute for Theoretical Physics, Kyoto University

Soichiro Shimamori Department of Physics, Osaka university

Harunobu Fujimura Department of Physics, Osaka university

## Quantum cosmology experiments in quantum Hall systems (21H05188)

How did our universe develop from its earliest moments? This is the major question of quantum cosmology, and to answer it great efforts have been made both in theory and in attempts to verify theory by observation of cosmic background radiation. It would be ideal if we could reproduce the origin and evolution of the universe in a laboratory and thereby experimentally verify the theory by controlling key parameters. Therefore, in this research project we aim at implementing quantum cosmology in the laboratory in a toy model which is a theoretically equivalent physical system to the early universe. In this way we seek to provide a rich playground for verification of quantum cosmology theory.

The actual physical system that we deal with comprises electrons in semiconductors. Semiconductor industry consists of state-of¬-the-art modern technologies such as ultra-high quality crystal growth technology, fine process technology, and electronics. In this project, using such mature technologies as a base, we implement toy models of quantum cosmology on a semiconductor chip using quantum Hall edges, which are an intriguing quantum many-body system. Through experiment and theory, we aim at unveiling the mechanism of the origin of the universe. More specifically, (1) we will establish advanced quantum measurement techniques and perform experiments on quantum Hall edges, and (2) examine quantum cosmology by collaborating with various fields of researchers from particle theory, mathematical physics, solid-state theory, quantum information, and cosmology

### Members in C02

[Principal Investigator]

Go Yusa Department of Physics, Tohoku University

[Co-Investigator]

Naokazu Shibata Department of Physics, Tohoku University

Masahiro Hotta Department of Physics, Tohoku University

Kazuya Yonekura Department of Physics, Tohoku University

[Research Collaborators]

Takaaki Mano National Institute for Materials Science

Kazuhiro Yamamoto Department of Physics, Kyushu University

Yasusada Nambu Department of Physics, Nagoya University

Chisa Hotta Graduate School of Arts and Sciences, University of Tokyo

Kazunori Nakayama Department of Physics, Tohoku University

Vladimir Umansky Weizmann Institute of Science

Koji Yamaguchi University of Waterloo

Kenichi Sasaki NTT Basic Research Laboratories

Kento Watanabe Department of Physics, Tohoku University

[Students]

Jun Tsujimura Department of Physics, Nagoya University

Yuki Sugiyama Department of Physics, Kyushu University

Yuka Kaku Department of Physics, Nagoya University

Yasuaki Hayafuchi Department of Physics, Tohoku University

Ryota Konno Department of Physics, Tohoku University

Reiji Kawada Department of Physics, Tohoku University

Yuki Osawa Department of Physics, Nagoya University

Donghyeon Kim Department of Physics, Tohoku University

Yunhyon Jeong Department of Physics, Tohoku University

Shun Kobayashi Department of Physics, Tohoku University

Takahiro Yokokura Department of Physics, Tohoku University

Kazunori Akiyama Department of Physics, Tohoku University

Ayaka Kondo Department of Physics, Tohoku University

Kairi Kaneta Department of Physics, Tohoku University

Yutaro Takahashi Department of Physics, Tohoku University

Felix Borchers Heidelberg University

Hiromasa Tajima Department of Physics, Nagoya University

[Past Members]

Akinori Kamiyama Department of Physics, Tohoku University

Ikuya Marumoto Department of Physics, Tohoku University

John Nicholas Moore Department of Physics, Tohoku University

## Quantum Cosmology from Quantum Information (21H05187)

The geometric formula of entanglement entropy (Ryu-Takayanagi formula), which connects quantum information and gravity theory, has led to the prediction that the universe in gravitational theory is a collection of quantum information, which has attracted worldwide attention. The aim of group C01 is to develop this prediction by introducing the viewpoint of quantum information into high energy theory, and to uncover the basic theory of the "dynamics of the creation of the universe (quantum universe)," which is one of the three problems of extreme universe. The foundation for this is the "gauge-gravity correspondence," or the hypothesis that the gravitational theory of the anti de Sitter universe is equivalent to a theory of quantum many-body system. The gauge-gravity correspondence is a powerful idea that has passed enormous verifications, but the basic principle of why this correspondence arises still remains unknown. If this principle is understood completely, it will be possible to elucidate the mechanism of the creation of the universe from nothing and eventually to construct the ultimate physical laws. The anti-de Sitter universe is a universe with negative curvature, while the real universe we live in and the process of creation of the universe are thought to have positive curvature, i.e., a de Sitter universe. In this research, we will first clarify the basic principle of gauge-gravity correspondence by combining the methods of quantum information theory and gauge-gravity correspondence, and then use it as a hint to extend the gauge-gravity correspondence beyond the anti-de Sitter universe to more general universes including the de Sitter universe. This will finally provide us with the fundamental theory for quantum cosmology.

### Members in C01

**[Principal Investigator]**

Tadashi Takayanagi Yukawa Institute for Theoretical Physics, Kyoto University

**[Co-Investigator]**

Yasuaki Hikida Yukawa Institute for Theoretical Physics, Kyoto University

Kazumi Okuyama Faculty of Science, Shinshu University

Yasuhiro Sekino Faculty of Engineering, Takushoku University

Shigeki Sugimoto Department of Physics, Kyoto University

**[International Research Collaborators]**

Shinsei Ryu Princeton U., USA

Beni Yoshida Perimeter Institute, Canada

**[ExU Postdoctoral Fellows(Research Collaborators)]
**Jonathan Harper Yukawa Institute for Theoretical Physics, Kyoto University

**[Research Collaborators]**

Kanato Goto Yukawa Institute for Theoretical Physics, Kyoto University

Tomotaka Kitamura Institute of Theoretical Physics, Rikkyo University

Shoichiro Miyashita Graduate School of Advanced Science and Engineering, Waseda University

Kazuhiro Sakai Institute of Physics, Meiji Gakuin University

Takahiro Uetoko National Institute of Technology, Kushiro College

Masamichi Miyaji Institute for Advanced Research, Nagoya University

Kenta Suzuki Institute of Theoretical Physics, Rikkyo University

Ali Mollabashi Yukawa Institute for Theoretical Physics, Kyoto University

Pawel Caputa Warsaw University

**[Post-doc Fellows]**

Shan-Ming Ruan Yukawa Institute for Theoretical Physics, Kyoto University

**[Graduate Students]
**Zixia Wei Yukawa Institute for Theoretical Physics, Kyoto University

Yusuke Taki Yukawa Institute for Theoretical Physics, Kyoto University

Taishi Kawamoto Yukawa Institute for Theoretical Physics, Kyoto University

Naoki Ogawa Yukawa Institute for Theoretical Physics, Kyoto University

Yu-ki Suzuki Yukawa Institute for Theoretical Physics, Kyoto University

Takashi Tsuda Yukawa Institute for Theoretical Physics, Kyoto University

Kazuki Doi Yukawa Institute for Theoretical Physics, Kyoto University

Hiroki Kanda Yukawa Institute for Theoretical Physics, Kyoto University

Masahide Sato Yukawa Institute for Theoretical Physics, Kyoto University

**[Past Members]
**Ibrahim Akal Yukawa Institute for Theoretical Physics, Kyoto University

**Yoshiki Sato Yukawa Institute for Theoretical Physics, Kyoto University**

## Understanding quantum black holes through the study of artificial quantum matter (21H05185)

A black hole gradually evaporates into thermal radiation, which is called the Hawking radiation, and finally disappears. This means that whatever information thrown into a black hole will eventually be “lost”. However, this contradicts the unitary time evolution, with the information on the initial state being conserved, in quantum mechanics. This apparent contradiction is called the “black hole information loss paradox”. Clarifying the mechanism by which information appears to be lost is one of the major objectives of this research area which aims to construct a theory of the “extreme universe” that integrates quantum theory and gravity theory.

The aim of group B02 is to promote the study of the quantum features of black holes, one of the key issues of the “extreme universe”, through the collaboration of cold atom experiments and theoretical studies. According to the gauge–gravity correspondence, the evaporation process of a black hole could correspond to the dynamics of a quantum matter.

Therefore, we will elucidate the nature of black holes by experimentally investigating the non-equilibrium dynamics of cold atomic systems in the laboratory which is a highly-controllable artificial quantum matter.

We will experimentally and theoretically perform research on (I) measurement-induced quantum phase transitions due to the effects of dissipation and/or measurement and (II) out-of-time-ordered correlation as the characterization of the delocalization of quantum information in cold atomic systems. In parallel, we will develop the theory for non-equilibrium phase transitions, methods for calculating non-equilibrium states using quantum computers, and evaluate the quantum entanglement in quantum many-body systems that are thought to correspond to quantum black holes and gauge gravity, such as the Sachdev-Ye-Kitaev model.

### Members in B02

**[Principal Investigator]**

Masaki Tezuka Department of Physics, Kyoto University

**[Co-Investigator]**

Shuta Nakajima Center for Quantum Information and Quantum Biology, Osaka University

Eriko Kaminishi Quantum Computing Center, Keio University

Takashi Mori RIKEN CEMS

Daisuke Yamamoto Department of Physics, Nihon University

**[International Research Collaborators]**

**[ExU Postdoctoral Fellows(Research Collaborators)]**

Kazuya Yamashita Department of Physics, Kyoto University

Giacomo Marmorini Department of Physics, Nihon University

**[Research Collaborators]**

Ippei Danshita Department of Physics, Kindai University

Kazuaki Takasan Department of Physics, University of Tokyo

Juan Pablo Bayona Pena Department of Physics, Kyoto University

**[Graduate Students]**

Kazuki Yamamoto Department of Physics, Kyoto University

Yuki Miyazaki Graduate School of Science and Engineering, Aoyama Gakuin University

Kou Gondaira Graduate School of Science and Engineering, Aoyama Gakuin University

## Black Holes and Singularities from Quantum Information (21H05186)

The aim of group B03 is to understand fundamental nature of quantum black holes by developing a new approach to quantum gravity that incorporates quantum information into general relativity. Black holes in general relativity are the simplest but one of the most mysterious objects in the universe since their basic constituent is merely the spacetime curvature, but they nevertheless possess thermodynamic properties, such as temperature and entropy. The possibility that a black hole can evaporate by emitting thermal Hawking radiation has raised the fundamental question, called the “black hole information paradox,” which concerns over general relativity and quantum information. The event horizon of a black hole is the causal boundary of domain of outer communications, whose structure and dynamics are governed by the null energy condition via the Einstein equations, and whose sectional area corresponds to the entropy, known as Bekenstein-Hawking entropy. The former aspect suggests that quantum mechanically corrected null energy conditions would play a significant role in understanding the structure and dynamics of quantum black holes. The latter aspect exhibits the close connection between the black hole entropy and quantum entanglement entropy, which characterizes the correlations between subsystems separated by a boundary surface in a larger quantum system. An increasing number of evidence shows that the black hole entropy can be described as an entanglement entropy via the gauge-gravity correspondence. Furthermore, recent development of the holographic principle indicates that geometric description of---not only a black hole event horizon but also---a various type of causal boundaries can admit the holographic description as a quantum entanglement via the Ryu-Takayanagi formula, which connects gravity with quantum information. It is thus anticipated that quantum aspects of gravity would become most tangible around causal boundaries and be described most effectively by using the language of quantum information theory. These observations form our view point of “extreme universe” that gravity/spacetime is a collection of quantum information. Based on these ideas, we will derive basic formulas that govern the dynamics of quantum black holes by unifying geometric and quantum information theoretic aspects of causal boundaries, and thereby attempt to establish a theoretical foundation for extreme universe.

### Members in B03

**[Principal Investigator]**

Akihiro Ishibashi(B03-PI) Department of Physics, Kindai University

**[Co-Investigator]**

Kengo Maeda Faculty of Engineering, Shibaura Institute of Technology

Keiju Murata Department of Physics, Nihon University

**[ExU Postdoctoral Fellow(Research Collaborators)]**

Yoshinori Matsuo Department of Physics, Kindai University

Shunichiro Kinoshita Department of Physics, Nihon University

**[Research Collaborators]**

Takashi Okamura Department of Physics, Kwansei Gakuin University

Gen Kimura Systems Engineering and Science, Shibaura Institute of Technology

Toshifumi Noumi Department of Physics, Kobe University

**[Post-doc Fellows]**

**[Graduate Students]**

Kodai Ueda Department of Physics, Kindai University

Daiki Yamaguchi Department of Physics, Kindai University

Satoshi Matsumoto Department of Physics, Kindai University

## Quantum information for theoretical physics (21H05183)

Quantum mechanics has mysterious properties not found in classical physics, such as quantum superposition, uncertainty principle, and no-cloning. The research field of quantum information exploits these mysterious properties to realize unprecedentedly high performance information processing technology. In particular, quantum computation, which enables high-speed calculations, and quantum cryptography, which enables various new cryptographic tasks not possible in classical physics, are major applications, and active research has been conducted in this field. In addition, the promotion of such research on quantum information technology will make it clear what can and cannot be done with quantum. This will also help us to understand why the mysterious quantum theory is the way it is. To truly understand why quantum theory is so mysterious is a long-standing goal of physicists that has existed since the time quantum theory was created.

Moreover, the results, insights, and techniques obtained from quantum information are proving to be useful in other physics as well. Various concepts such as AdS/CFT in particle theory, distribution functions in statistical physics, tensor networks in condensed matter physics, and quantum randomness in black holes can be studied from a new perspective through quantum information.

This project group is composed of experts in quantum information, and its role is to provide other groups with the necessary "language" to achieve the overall goal of creating physical laws of the extreme universe based on quantum information, and to refine the language by deepening the basic theory of quantum information itself.

### Members in A01

**[Principal Investigator]**

Tomoyuki Morimae Yukawa Institute for Theoretical Physics, Kyoto University

**[Co-Investigator]**

Yoshifumi Nakata Yukawa Institute for Theoretical Physics, Kyoto University

Koji Azuma NTT Basic Research Laboratories

Francesco Buscemi Department of Mathematical Informatics, Nagoya University

**[ExU Postdoctoral Fellows(Research Collaborators)]**

Arthur Parzygnat Department of Mathematical Informatics, Nagoya University

**[Research Collaborators]**

Andrew Darmawan Yukawa Institute for Theoretical Physics, Kyoto University

Michele Dall’Arno Yukawa Institute for Theoretical Physics, Kyoto University

Hayata Yamasaki University of Vienna

Go Kato Advanced ICT Research Institute, NICT

**[Post-doc fellow]**

Aditya Nema Department of Mathematical Informatics, Nagoya University

**[Graduate students]**

Ryu Hayakawa Yukawa Institute for Theoretical Physics, Kyoto University

Taiga Hiroka Yukawa Institute for Theoretical Physics, Kyoto University

Misaki Yonekawa Yukawa Institute for Theoretical Physics, Kyoto University

Takumi Kagitani Yukawa Institute for Theoretical Physics, Kyoto University

Takaya Matsuura Graduate School of Engineering, The University of Tokyo

Shiro Tamiya Graduate School of Engineering, The University of Tokyo