Emergence of the non-Hermitian topology in generalized eigenvalue problems with Hermitian matrices
Mon. March 6, 11:54 a.m. – 12:06 p.m. GMT-8
Room 318

Topological band theory has been studied as one of the central issues of condensed matter physics in these fifteen years. It has been initiated as the eigenvalue problems of a Hermitian matrix [1,2], which has revealed many non-trivial phenomena such as bulk-boundary correspondence [3]. Notably, recent studies have extended the framework of the topological band theory to the non-Hermitian eigenvalue problems [4,5,6]. This extension reveals the existence of the topological phenomena unique to the non-Hermitian systems.
In this talk, we attempt a further extension of the topological band theory: extension of topological band theory to the generalized eigenvalue problem [7]. In particular, we elucidate the emergence of the symmetry-protected non-Hermitian topological band structure without non-Hermitian matrices. After that discussion, we analyze a toy model and apply our theory to an optical system.

[1] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
[2] X. -L. Qi and S. -C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[3] Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[4] K. Esaki, M. Sato, K. Hasebe, and M. Kohmoto, Phys. Rev. B 84, 205128 (2011).
[5] H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018).
[6] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018).
[7] T. Isobe, T. Yoshida, and Y. Hatsugai, Phys. Rev. B 104, L121105 (2021).

Presented By
Takuma Isobe (University of Tsukuba)
Authors
Takuma Isobe (University of Tsukuba)
Tsuneya Yoshida (Kyoto university)
Yasuhiro Hatsugai (University of Tsukuba)

Correlation effects on non-Hermitian topological classifications
Thu. March 9, 12:30 p.m. – 12:42 p.m. GMT-8
Room 217/218

Extensive studies in these years have discovered a variety of exotic phenomena for non-Hermitian systems[1-4] such as the emergence of exceptional points[5] and skin effects[6]. So far, most of the works have focused on non-interacting systems. However, recent the development of technology allows to fabricate non-Hermitian correlated systems for cold atoms[7], which poses the following question: correlation effects on non-Hermitian topology.
In this paper, we address this issue with particular emphasis on the classification of non-Hermitian point-gap topology in zero- and one dimension. Our analysis elucidates that correlations results in the reduction of topological classifications[8,9].

Presented By
Tsuneya Yoshida (Kyoto Univ.)
Authors
Tsuneya Yoshida (Kyoto Univ.)
Yasuhiro Hatsugai (University of Tsukuba)

Similarities and differences in flat-band models with randomness detected by machine learning
Tue. March 7, 9:24 a.m. – 9:36 a.m. GMT-8
Room 417

Since Anderson localization was proposed, disordered electron systems have been studied extensively. As a recent development, systems that have characteristic electronic structures in the clean limit have been actively studied. For example, the flat-band (FB) systems have attracted attention because of their characteristic behavior to disorder [1,2]. Besides, it has also been shown, from the technical point of view, that machine learning (ML) is a useful method for identifying characteristic real-space distributions of wavefunctions. In our previous work, we studied the phase classification of FB states of molecular orbital (MO) models by ML [3]. A MO model is a model constructed on the basis of a linear combination of atomic orbitals, and it is known that macroscopic degeneracy remains even in the presence of randomness [4,5,6].
Based on these backgrounds, in this presentation, we compare a MO model with another random FB model. Specifically, we report the results of the ML study for the FB states of a random MO model and a model in which random potentials are introduced into the conventional FB model. In particular, we elaborate on how the choice of training data affects the output. We discuss the similarities and differences between the above two FB models inferred from the results.

[1] M. Goda, et al., PRL 96, 126401 (2006).
[2] J. T. Chalker, et al., PRB 82, 104209 (2010).
[3] T. Kuroda, et al., JPSJ 91, 044703 (2022).
[4] Y. Hatsugai, et al., EPL 95 20003 (2011).
[5] T. Mizoguchi, et al., EPL 127 47001 (2019).
[6] Y. Hatsugai, Ann Phys 168453 (2021).

Presented By
Takumi Kuroda (University of Tsukuba)
Authors
Takumi Kuroda (University of Tsukuba)
Tomonari Mizoguchi (University of Tsukuba)
Yasuhiro Hatsugai (University of Tsukuba)