Preprints & Comments:

21. Yoshiki Sano, Daichi Takikawa, Masahiro O. Takahashi, Masahiko G. Yamada, Takeshi Mizushima, Satoshi Fujimoto,

“Nonreciprocal heat transport in the Kitaev chiral spin liquid”,

arXiv:2408.15564 [cond-mat.str-el]

This research was initially developed from a conversation with Prof. Morimoto (Applied Physics Department), in which we both agreed that this was interesting. Dr. Takikawa and Mr. Sano took the lead in the research. It was a good starting point for moving in various directions, such as the non-oppositeness of the Kitaev model in chiral lattices as a developmental topic.

20. K. Imamura, Y. Mizukami, O. Tanaka, R. Grasset, M. Konczykowski, N. Kurita, H. Tanaka, Y. Matsuda, M. G. Yamada, K. Hashimoto, T. Shibauchi,

“Scaling of Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet α-RuCl₃”,

arXiv:2306.17380 [cond-mat.str-el]

The research we were conducting in collaboration with the experimental group (led by Prof. Shibauchi) was published for the first time. I am in charge of theoretical data analysis. Based on the Kitaev-Anderson spin liquid research of the past, we are discussing how disorder works in quantum spin liquids based on experimental results.

19. Masahiko G. Yamada, Takumi Sanno, Masahiro O. Takahashi, Yutaka Akagi, Hidemaro Suwa, Satoshi Fujimoto, Masafumi Udagawa,

“Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver”,

arXiv:2212.13267 [cond-mat.str-el]

MPRG is a versatile quantum many-body solver that can simulate a complete infinite system in any dimension at zero and finite temperatures. Since MPRG does not use variational methods, it can also simulate non-Hermitian systems. For example, we analyzed the Yang-Lee model, a non-Hermitian quantum many-body system, and understood the correct critical phenomena.

18. Masahiro O. Takahashi, Masahiko G. Yamada, Masafumi Udagawa, Takeshi Mizushima, Satoshi Fujimoto,

“Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid”,

arXiv:2211.13884 [cond-mat.str-el]

This research project was carried out with the help of Dr. Takahashi. Recently, there has been a lot of activity in STM experiments and proposals for experiments on Kitaev magnetic bodies. This proposal suggests that we may see non-local correlations between Majorana quasiparticles through this. In particular, this “quantum teleportation” has the potential to be seen in the spin-spin correlations between spin defects, and it is possible to prove their existence experimentally through this.

17. Takumi Sanno, Masahiko G. Yamada, Takeshi Mizushima, Satoshi Fujimoto,

“Engineering Yang-Lee anyons via Majorana bound states”,

arXiv:2208.01803 [cond-mat.str-el]

This research project was carried out with the help of Dr. Sanno. Rather than trying to realize Yang-Lee anyons themselves, the focus was on implementing the “Yang-Lee model” that would serve as a stage for it by engineering a non-Hermitian Hamiltonian. There were some twists and turns along the way, such as finding some imperfections in the methods used in previous research on non-Hermitian systems, but I'm glad we could bring it to fruition.

16. Yukiyasu Moriya, Taiki Matsushita, Masahiko G. Yamada, Takeshi Mizushima, Satoshi Fujimoto,

“Intrinsic Anomalous Thermal Hall Effect in the Unconventional Superconductor UTe2”,

arXiv:2205.11848 [cond-mat.supr-con]

I wasn't deeply involved in this research, but I helped when a student asked me how to do numerical calculations for heat conduction. After first teaching them how to calculate Chern numbers, I provided general support for the numerical calculations, including how to visualize the Berry curvature.

15. Masahiko G. Yamada, Satoshi Fujimoto,

“Thermodynamic signature of the SU(4) spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem”,

arXiv:2111.14470 [cond-mat.str-el]

The contents are divided into two parts, and in the first half, we thoroughly investigated the thermodynamic properties of the SU(4) Heisenberg model on the honeycomb lattice using the cTPQ method. We proposed that this model can be realized in α-ZrCl₃, so we think that this will be useful for identifying whether or not these candidate materials realize the SU(4) Heisenberg model. In the second half, we used a new proof to extend the LSM theorem to two dimensions. We also discussed the possibility that the SU(4) Heisenberg model on the honeycomb lattice is a gapped spin liquid or a non-trivial topological phase.

14. Masahiko G. Yamada, Satoshi Fujimoto,

“Quantum liquid crystals in the finite-field KΓ model for α-RuCl₃”,

arXiv:2107.03045 [cond-mat.str-el]

This is an extended version of the paper (11). The difference is that we have derived the effective Hamiltonian starting from the KΓ model in a first-principles manner. In addition to the nematic transition that we discussed previously, we have discovered a new phase transition that gives rise to the Kekulé order. In this Kekulé phase, Z₃ vortices, which are defined as the intersection of domain walls, have the property of binding the Majorana zero mode, and there is the possibility that they can be applied to quantum computation.

13. Daichi Takikawa, Masahiko G. Yamada, Satoshi Fujimoto,

“Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid”,

arXiv:2104.11115 [cond-mat.str-el]

This is also a paper written while supervising a student. By focusing on the edge of the Kitaev model, we noticed that the extra gauge field Majorana fermions can be treated in the same way as itinerant Majorana fermions. Using this, we can directly calculate correlations of spin operators that cannot typically be calculated, and for example, we can calculate the linear response of spin currents localized at the edge. In this study, we used the edge spin Seebeck effect and discovered that the temperature dependence of the Drude weight exhibits universality. This is consistent with the predictions of conformal field theory, and it can be said that it is one way to detect Majorana fermions of the Kitaev model.

12. Masahiko G. Yamada, Masaki Oshikawa, George Jackeli,

“SU(4)-Symmetric Quantum Spin-Orbital Liquids on Various Lattices”,

arXiv:2103.17076 [cond-mat.str-el]

Full paper version of PRL paper (4).

11. Masahiro O. Takahashi, Masahiko G. Yamada, Daichi Takikawa, Takeshi Mizushima, Satoshi Fujimoto,

“Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields”,

arXiv:2101.05959 [cond-mat.str-el]

This is the first paper we wrote while supervising students. We proposed a theoretical scenario to explain the signs of the nematic transition observed in α-RuCl₃ in high magnetic fields. The scenario is that there is a possibility of a phase transition from the model of free Majorana fermions described initially by the Kitaev chiral spin liquid (B-phase) to the Z₂ spin liquid (A-phase) with nematic order due to the four-body interaction of Majorana fermions. There are several possible types of Majorana four-body interactions, so it's not easy to say that this is happening in reality. Still, in this case, we have predicted the existence of a topological nematic transition, in which a topological transition and a nematic transition co-occur, mainly if the interaction is of the Y-shape type.

10. Masahiko G. Yamada, Satoshi Fujimoto,

“Electric probe for the toric code phase in Kitaev materials through the hyperfine interaction”,

arXiv:2012.08825 [cond-mat.str-el]

This is a paper that was completed in a short period. In recent experiments in the Shibauchi Laboratory, signs of a nematic transition were observed in α-RuCl₃ in the high-magnetic-field region. Precise measurement of the (spin) nematic transition is challenging, but we proposed performing it by measuring the electric quadrupole moment (EQM). Usually, spins with j=1/2 do not have EQM, but because the j=3/2 state appears in the virtual state during the second-order perturbation, it gives a non-zero contribution to EQM. We have proposed a new method for detecting (spin) nematic phases that is fundamentally different from conventional methods.

9. Masahiko G. Yamada,

“Topological insulator in Kitaev spin liquids”,

arXiv:2005.03399 [cond-mat.str-el]

The content of this paper is that a topological insulator phase has been realized in the Kitaev spin liquid. Note that the topological insulator is a narrow-sense topological insulator protected by time-reversal symmetry. Kitaev and others have already realized broad-sense topological insulators (such as Chern insulators). On the other hand, it has been thought that (narrowly defined) topological insulators do not exist in the Kitaev spin liquid according to the “topological periodic table.” However, because the symmetry is projective in the spin liquid, a new class of topological insulators is born following the projectivity of time-reversal symmetry. We have found a new class of topological insulator phase in the Kitaev model on the square-octagon lattice.

8. Masahiko G. Yamada,

“Kitaev-Anderson spin liquid”,

arXiv:2004.06257 [cond-mat.str-el]

This is my first paper to be published as a single-authored contribution. The question of what happens when a disorder is introduced into a quantum spin liquid has been studied for many years, but to be honest, it has been challenging to understand it because no model could be solved instantly. The Kitaev model is an exceptionally solvable model of a quantum spin liquid, so it is possible to investigate the effects of disorder in detail. Specifically, we used the kernel polynomial method to calculate the thermal Hall effect. Occasionally, we showed that the thermal Hall coefficient, which quantizes in the clean limit, changes immediately to a different, smaller value as more disorder is introduced. This is because the topological edge states become localized due to the Anderson localization, and the bulk also shows a characteristic change from a thermal insulator to a thermal conductor and then to a thermal insulator. In addition, a universal change also appears in the DOS, which may be a characteristic of the Kitaev spin liquid with a disorder.

7. Masahiko G. Yamada,

“PhD Thesis: Searching for an emergent SU(4) symmetry in real materials”,

arXiv:2004.01716 [cond-mat.str-el]

An arXiv version of the PhD thesis.

6. Masahiko G. Yamada, Yasuhiro Tada,

“Quantum valence bond ice theory for proton-driven quantum spin-dipole liquids”,

arXiv:1903.03567 [cond-mat.str-el]

It is thought that κ-H₃(Cat-EDT-TTF)₂ is not only an organic quantum spin liquid but also a new quantum spin-dipole liquid, where spin and hydrogen (proton) fluctuations are correlated. However, in the first place, there is no known theoretical model of a hybrid quantum liquid in which spin and proton simultaneously exist in a quantum liquid state, and we do not even know how to define such a state. Therefore, as a first step, we created a theoretical model that could be solved and computed numerically. Then, we theoretically proved the existence of a quantum spin-dipole liquid state. We then proposed that the entanglement entropy between electrons and protons could be used to characterize its feature.

5. Masahiko G. Yamada, George Jackeli,

“Magnetic and Electronic Properties of Spin-Orbit Coupled Dirac Electrons on a (001) Thin Film of Double Perovskite Sr₂FeMoO₆”,

arXiv:1711.08674 [cond-mat.str-el]

This is the research that was completed at the earliest, but for various reasons, it was delayed in being made into a paper. The proposal is that double perovskite becomes more stable when made into a thin film, thanks to its spin-orbit coupling. A flat band appears directly above the Fermi surface, and there is a possibility that the Wigner crystal can be realized by doping.

4. Masahiko G. Yamada, Masaki Oshikawa, George Jackeli,

“Emergent SU(4) Symmetry in α-ZrCl₃ and Crystalline Spin-Orbital Liquids”,

arXiv:1709.05252 [cond-mat.str-el]

It is thought that the Standard Model can describe the microscopic fundamental laws of the universe, i.e., the U(1)xSU(2)xSU(3) gauge theory, within the range of the energy scale that can be observed with current technology. On the other hand, SU(4) is not included in the subgroup of this gauge theory or the group that represents special relativity, and there is no (already discovered) SU(4) symmetry as a fundamental symmetry of the universe. However, since electrons in matter behave differently from elementary particles, it is possible to engineer SU(4) symmetry in the low-energy effective Hamiltonian of matter. We proposed that such emergent SU(4) symmetry exists in the material system like α-ZrCl₃ and that this material and related materials become quantum spin-orbital liquids thanks to its emergent symmetry.

3. Masahiko G. Yamada, Vatsal Dwivedi, Maria Hermanns,

“Dirac nodes and nodal chains in 3D Kitaev spin liquids”,

arXiv:1707.00898 [cond-mat.str-el]

In this paper, we analytically determine the ground state of the Kitaev model on the 8².10-a and (10,3)-d lattices, which can be realized in MOFs. Although this is a highly specialized topic, these models are characterized by the fact that the lattice has a nonsymmorphic symmetry and phenomena that cannot be explained by the general (3D) Kitaev model theory. This is probably the first time that it has been rigorously shown that a spin liquid has a 3D Dirac dispersion at low energy and that the symmetry of the crystal protects nodal lines. However, this is not a free fermion system but a strongly correlated one, showing a strong quantum entanglement between localized spins.

2. Masahiko G. Yamada, Hiroyuki Fujita, Masaki Oshikawa,

“Designing Kitaev spin liquids in metal-organic frameworks”,

arXiv:1605.04471 [cond-mat.str-el]

The Kitaev model, an exactly solvable model of topological phases and quantum spin liquids, is extremely important from the perspective of applications to topological quantum computation, etc. However, most inorganic candidate materials, such as iridium oxides and ruthenium compounds, exhibit classical magnetic ordering at low temperatures and do not have a quantum spin liquid ground state. This is said to be mainly due to direct interactions between metal ions. In this study, we again focused on MOFs and found that MOFs composed of ruthenium and oxalate or tetraaminopyrazine are new candidate materials for the Kitaev model. We discovered that MOFs containing organic matter are more advantageous than inorganic matter in terms of suppressing direct interactions and that the degeneracy of the HOMO gives rise to the Kitaev interaction. Another new advantage of using MOFs is that it has expanded the possibilities for controlling parameters and realizing topological phases with gaps, as well as for realizing three-dimensionally extended Kitaev models.

1. Masahiko G. Yamada, Tomohiro Soejima, Naoto Tsuji, Daisuke Hirai, Mircea Dincă, Hideo Aoki,

“First-Principles Design of a Half-Filled Flat Band of the Kagome Lattice in Two-Dimensional Metal-Organic Frameworks”,

arXiv:1510.00164 [cond-mat.str-el]

Flat-band ferromagnetism, which explains the origin of ferromagnetism in terms of electron correlation, has long been predicted from the perspective of mathematical physics. Still, no material that exhibits this phenomenon in a two-dimensional lattice system was known. This study focused on a two-dimensional metal-organic framework (MOF) with a Kagome lattice structure. We proposed the possibility that trans-Au-THTAP realizes flat-band ferromagnetism within the framework of the tight-binding (TB) model and density functional theory (DFT). This memorable first paper proves the high designability of two-dimensional MOFs.