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Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
| Title: | Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms |
| Authors: | Mochizuki, Ken Browse this author | | Hatano, Naomichi Browse this author | | Feinberg, Joshua Browse this author | | Obuse, Hideaki Browse this author →KAKEN DB |
| Issue Date: | 1-Jul-2020 |
| Publisher: | American Physical Society (APS) |
| Journal Title: | Physical Review E |
| Volume: | 102 |
| Issue: | 1 |
| Start Page: | 012101 |
| Publisher DOI: | 10.1103/PhysRevE.102.012101 |
| Abstract: | We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems. |
| Rights: | Copyright (2020) by The American Physical Society. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/79102 |
| Appears in Collections: | 工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 小布施 秀明
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