業績情報

• Alpha Zero for Physics: Application of Symbolic Regression with Alpha Zero to find the analytical methods in physics
  Yoshihiro Michishita
  2023年11月
  Machine learning with neural networks is now becoming a more and more
  powerful tool for various tasks, such as natural language processing, image
  recognition, winning the game, and even for the issues of physics. Although
  there are many studies on the application of machine learning to numerical
  calculation and assistance of experiments, the methods of applying machine
  learning to find the analytical method are poorly studied. In this paper, we
  propose the frameworks of developing analytical methods in physics by using the
  symbolic regression with the Alpha Zero algorithm, that is Alpha Zero for
  physics (AZfP). As a demonstration, we show that AZfP can derive the
  high-frequency expansion in the Floquet systems. AZfP may have the possibility
  of developing a new theoretical framework in physics.
  arXiv ID：arXiv:2311.12713
• Machine-learning-assisted construction of appropriate rotating frame
  Yoshihiro Michishita
  2022年11月
  Machine learning with neural networks is now becoming a more and more
  powerful tool for various tasks, such as natural language processing, image
  recognition, winning the game, and even for the issues of physics. Although
  there are many studies on the application of machine learning to numerical
  calculation and the assistance of experimental detection, the methods of
  applying machine learning to find the analytical method are poorly studied. In
  this letter, we propose methods to use machine learning to find the analytical
  methods. We demonstrate that the recurrent neural networks can ``derive'' the
  Floquet-Magnus expansion just by inputting the time-periodic Hamiltonian to the
  neural networks, and derive the appropriate rotating frame in the
  periodically-driven system. We also argue that this method is also applicable
  to finding other theoretical frameworks in other systems.
  arXiv ID：arXiv:2211.15269
• Quantum metric on the Brillouin Zone in correlated electron systems and its relation to topology for Chern insulators　　　　　　　　　　　　　　　
  Takahiro Kashihara; Yoshihiro Michishita; Robert Peters
  2022年11月
  Geometric aspects of physics play a crucial role in modern condensed matter
  physics. The quantum metric is one of these geometric quantities which defines
  the distance on a parameter space and contributes to various physical
  phenomena, such as superconductivity and nonlinear conductivity. Despite its
  importance, the quantum metric in interacting systems is poorly understood. In
  this paper, we introduce a generalized quantum metric(GQM) on the Brillouin
  zone for correlated electron systems. This quantum metric is based on the
  optical conductivity that is written by single-particle Green's functions. We
  analytically prove that this definition is equivalent to the existing
  definition of the quantum metric in noninteracting systems and that it is
  positive semi-definite as necessary for a metric. Furthermore, we point out the
  relationship between the GQM and the Chern number in interacting systems. We
  then numerically confirm these properties of the GQM in the Qi-Wu-Zhang model
  with and without interaction. We believe that the GQM will be a step toward
  generalizing the quantum metric to the interacting regime.
  DOI：https://doi.org/10.1103/PhysRevB.107.125116
  DOI ID：10.1103/PhysRevB.107.125116, arXiv ID：arXiv:2211.07924
• Dissipation and geometry in nonlinear quantum transports of multiband electronic systems　　　　　　　　　　　　　　　
  Yoshihiro Michishita; Naoto Nagaosa
  2022年04月
  Nonlinear responses in condensed matters attract recent intensive interest
  because they provide rich information about the materials and hold the
  possibility of being applied in diodes or high-frequency optical devices.
  Nonlinear responses are often closely related to the multiband nature of the
  system which can be taken into account by the geometric quantities such as the
  Berry curvature as shown in the nonlinear Hall effect. Theoretically, the
  semi-classical Boltzmann treatment or the reduced density matrix method have
  been often employed, in which the effect of dissipation is included through the
  relaxation time approximation. In the diagrammatic method, the relaxation is
  treated through the imaginary part of the self-energy of the Green function and
  the consequent broadening of the spectral function for the integration over the
  real frequency. Therefore, the poles of the Green function do not play explicit
  pole when there is finite dissipation. In this paper, in stark contrast to this
  conventional picture, we show that the poles of the Green function determine
  mostly the nonlinear response functions with dissipation, which leads to the
  terms with the Fermi distribution function of complex argument and results in
  the dissipation-induced geometric term. We elucidate the geometric origin of
  the nonreciprocal conductivity, which is related to the Berry curvature
  generalized to the higher derivative. Finally, we derive the analytical results
  on the geometric terms of the nonlinear conductivities in the type-I and
  type-II Weyl Hamiltonian to demonstrate their crucial roles.
  DOI：https://doi.org/10.1103/PhysRevB.106.125114
  DOI ID：10.1103/PhysRevB.106.125114, arXiv ID：arXiv:2204.08365
• Surface exceptional points in a topological Kondo insulator　　　　　　　　　　　　　　　
  Robert Peters; Kazuhiro Kimura; Yoshihiro Michishita; Tsuneya Yoshida; Norio Kawakami
  2021年09月
  Correlated materials have appeared as an arena to study non-Hermitian effects
  as typically exemplified by the emergence of exceptional points. We show here
  that topological Kondo insulators are an ideal platform for studying these
  phenomena due to strong correlations and surface states exhibiting a nontrivial
  spin texture. Using numerical simulations, we demonstrate the emergence of
  exceptional points in the single-particle Green's function on the surface of
  the material while the bulk is still insulating. We reveal how quasiparticle
  states with long lifetimes are created on the surface by non-Hermitian effects
  while the Dirac cones are smeared, which explains the surface Kondo breakdown
  at which heavy Dirac cones disappear from the single-particle spectrum and are
  replaced by light states. We further show how the non-Hermiticty changes the
  spin texture inherent in the surface states, which might help identify
  exceptional points experimentally. Besides confirming the existence of
  non-Hermitian effects on the surface of a topological Kondo insulator, this
  paper demonstrates how the eigenstates and eigenvalues of the effective
  non-Hermitian matrix describing the single-particle Green's function help
  understand the properties of correlated materials.
  DOI：https://doi.org/10.1103/PhysRevB.104.235153
  DOI ID：10.1103/PhysRevB.104.235153, arXiv ID：arXiv:2109.09298
• Effects of strong correlations on the nonlinear response in Weyl-Kondo semimetals　　　　　　　　　　　　　　　
  Akira Kofuji; Yoshihiro Michishita; Robert Peters
  2021年03月
  Nonlinear responses give rise to various exciting phenomena, which are
  forbidden in linear responses. Among them, one of the most fascinating
  phenomena is the recently observed giant spontaneous Hall effect in
  $\mathrm{Ce_{3}Bi_{4}Pd_{3 } }$. This material is a promising candidate for a
  Weyl-Kondo semimetal, and this experiment implies that strong correlation
  effects can enhance the nonlinear Hall effect. However, most theoretical
  studies on nonlinear responses have been limited to free systems, and the
  connection between nonlinear responses and strong correlation effects is poorly
  understood. Motivated by these experiments and recent theoretical advances to
  analyze strong correlation effects on the nonlinear response, we study a
  periodic Anderson model describing $\mathrm{Ce_{3}Bi_{4}Pd_{3 } }$ using the
  dynamical mean-field theory. We calculate the nonlinear longitudinal
  conductivity and the nonlinear Hall conductivity using the Kubo formula
  extended to the nonlinear response regime and clarify their temperature
  dependences. We numerically show that strong correlations can enhance nonlinear
  conductivities, and we conclude that the magnitude of the experimentally
  observed giant nonlinear Hall effect can be explained by strong correlation
  effects.
  DOI：https://doi.org/10.1103/PhysRevB.104.085151
  DOI ID：10.1103/PhysRevB.104.085151, arXiv ID：arXiv:2103.03522
• Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems　　　　　　　　　　　　　　　
  Yoshihiro Michishita; Robert Peters
  2020年12月
  Nonlinear responses in condensed matter are intensively studied because they
  provide rich information about materials and hold the possibility of being
  applied in diodes or high-frequency optical devices. While nonlinear responses
  in noninteracting models have been explored widely, the effect of strong
  correlations on the nonlinear response is still poorly understood, even though
  it has been suggested that correlations can enhance the nonlinear response. In
  this work, we first give an analytical derivation of nonlinear responses using
  the Green's function methods at finite temperature. Then, we discuss the
  difficulties of considering dissipation using conventional methods, such as the
  reduced density matrix method. We reveal that the relaxation time approximation
  leads to severe limitations when considering optical responses. Finally, we
  demonstrate that correlation effects, such as the renormalization of the band
  structure and different lifetime in orbitals or sublattices, can significantly
  enhance nonlinear responses and can even change the sign of the nonlinear
  conductivity.
  DOI：https://doi.org/10.1103/PhysRevB.103.195133
  DOI ID：10.1103/PhysRevB.103.195133, arXiv ID：arXiv:2012.10603
• Equivalence of the effective non-hermitian Hamiltonians in the context of open quantum systems and strongly-correlated electron systems　　　　　　　　　　　　　　　
  Yoshihiro Michishita; Robert Peters
  2020年01月
  Recently, it has become clear that non-hermitian phenomena can be observed
  not only in open quantum systems experiencing gain and loss but also in
  equilibrium single-particle properties of strongly correlated systems. However,
  the circumstances and requirements for the emergence of non-hermitian phenomena
  in each field are entirely different. While the implementation of postselection
  is a significant obstacle to observe non-hermitian phenomena in open quantum
  systems, it is unnecessary in strongly correlated systems.
  Until now, a relation between both descriptions of non-hermitian phenomena
  has not been revealed. In this paper, we close this gap and demonstrate that
  the non-hermitian Hamiltonians emerging in both fields are identical, and we
  clarify the conditions for the emergence of a non-hermitian Hamiltonian in
  strongly correlated materials. Using this knowledge, we propose a method to
  analyze non-hermitian properties without the necessity of postselection by
  studying specific response functions of open quantum systems and strongly
  correlated systems.
  DOI：https://doi.org/10.1103/PhysRevLett.124.196401
  DOI ID：10.1103/PhysRevLett.124.196401, arXiv ID：arXiv:2001.09045
• Relation between exceptional points and the Kondo effect in $f$-electron materials　　　　　　　　　　　　　　　
  Yoshihiro Michishita; Tsuneya Yoshida; Robert Peters
  2019年05月
  We study the impact of nonhermiticity due to strong correlations in
  f-electron materials. One of the most remarkable phenomena occurring in
  nonhermitian systems is the emergence of exceptional points at which the
  effective nonhermitian Hamiltonian becomes non-diagonalizable. We here
  demonstrate that Kondo temperature is related to the temperature at which
  exceptional points appear around the Fermi level. For this purpose, we study
  the periodic Anderson model with local and nonlocal hybridization in the
  insulating and metallic regimes. By analyzing the effective nonhermitian
  Hamiltonian, which describes the single-particle spectral function, and the
  temperature dependence of the screening of the magnetic moment, from which the
  Kondo temperature can be found, we show that exceptional points appear at the
  temperature at which the magnetic moment is screened. These results suggest
  that the well-known crossover between localized and itinerant f electrons in
  $f$-electron materials is related to the emergent exceptional points in the
  single-particle spectral function.
  DOI：https://doi.org/10.1103/PhysRevB.101.085122
  DOI ID：10.1103/PhysRevB.101.085122, arXiv ID：arXiv:1905.12287
• Impact of the Rashba Spin Orbit Coupling on $f$-electron Materials　　　　　　　　　　　　　　　
  Yoshihiro Michishita; Robert Peters
  2018年12月
  The combination of strong spin orbit coupling and strong correlations holds
  tremendous potential for interesting physical phenomena as well as applications
  in spintronics and quantum computation. In this context, we here study the
  interplay between the Rashba spin-orbit coupling (RSOC) and the Kondo screening
  in noncentrosymmetric $f$-electron materials. We show that the Kondo coupling
  of the $f$-electrons becomes anisotropic at high temperatures due to the RSOC.
  However, an isotropic Kondo effect is restored at low temperature which leads
  to a complete Kondo screening. We furthermore demonstrate that the Kondo effect
  has influence on the Rashba splitting in the band structure, which becomes
  temperature dependent. Although the $f$-electrons are localized at high
  temperature, a helical spin polarization of the conduction band emerges due to
  the scattering with the $f$-electrons. With decreasing temperature, the Kondo
  screening occurs, which leads to drastic changes in the band structure.
  Remarkably, these changes in the band structure depend on the helical spin
  polarization. For strong RSOC, we observe that the hybridization gap of one of
  the helical bands is closed at low temperature and a helical half-metal is
  formed.
  DOI：https://doi.org/10.1103/PhysRevB.99.155141
  DOI ID：10.1103/PhysRevB.99.155141, arXiv ID：arXiv:1812.10888

• 「スケールの分離」を主軸とした物理と機械学習の融合的手法の開発　　　　　　　　　　　　　　　
  日本学術振興会, 科学研究費助成事業, 若手研究, 2024年04月01日 - 2026年03月31日
  道下 佳寛, 国立研究開発法人理化学研究所
  配分額（総額）：4680000, 配分額（直接経費）：3600000, 配分額（間接経費）：1080000
  課題番号：24K16983
• Machine-Learning-assisted Construction of Appropriate Frame　　　　　　　　　　　　　　　
  日本学術振興会, 科学研究費助成事業, 学術変革領域研究(A), 2023年04月01日 - 2025年03月31日
  道下 佳寛, 国立研究開発法人理化学研究所
  配分額（総額）：2470000, 配分額（直接経費）：1900000, 配分額（間接経費）：570000
  課題番号：23H04527
  講演・口頭発表等ID：47396388
• 強相関電子系における非平衡現象に対する新規数値計算手法の提案及び微視的機構の解明　　　　　　　　　　　　　　　
  日本学術振興会, 科学研究費助成事業, 特別研究員奨励費, 2020年04月24日 - 2022年03月31日
  道下 佳寛, 京都大学
  配分額（総額）：1700000, 配分額（直接経費）：1700000
  前年度の研究(散逸・繰り込みの非線形応答に及ぼす影響の解析)に引き続き、散逸の効果を特に幾何学的な立場から解析した。
  まずGreen関数を用いた表式から出発し、実周波数積分を複素平面上の経路積分に置き換える事で、フェルミ分布関数由来の松原振動数の極からの寄与と、バンド固有値由来のグリーン関数の極からの寄与に分ける事が出来る。既存の研究で得られていた結果は、グリーン関数の極からの寄与について散逸がゼロの極限を取ったものと一致する。
  散逸が無視できない場合に、線形の場合は松原からの寄与が大きく残るが、一方で(２次の)非線形応答においては他の項に比べて非常に小さくなることが分かった。２次の非線形応答においては空間反転対称性が必要であり、その情報は、バンドの幾何学的な項にエンコードされているが、松原振動数の極からの寄与は、この情報がほとんど見えないためにほとんど寄与しない。
  つまり非線形応答においてはグリーン関数の極からの寄与のみ着目すれば、散逸の効果を取り込めている事になる。この時、散逸を表す自己エネルギーの虚部により、(準粒子の寿命を反映して)バンド固有値は複素数となり、フェルミ分布関数に複素数が代入される。結果フェルミ分布関数の虚部が生まれ、そこから新たな幾何学的な寄与として、Christoffel symbol termとgeneralized Berry curvature termが生まれる事が分かった。我々はこれらの項をdissipation-induced geometric term(散逸により新たに誘起される幾何学項)と名付けた。前者は非線形Drude項の他バンド補正を与え、後者は非相反応答の根源となる。
  またWeylHamiltonianにおいて非線形応答の特異な化学ポテンシャル依存性を発見した。これは実験におけるワイル点及びそのタイプの同定に非常に役立つと思われる。
  課題番号：20J12265
  講演・口頭発表等ID：47396509