Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms

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Autori principali: Mochizuki, Ken, Hatano, Naomichi, Feinberg, Joshua, Obuse, Hideaki
Natura: Preprint
Pubblicazione: 2020
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author Mochizuki, Ken
Hatano, Naomichi
Feinberg, Joshua
Obuse, Hideaki
author_facet Mochizuki, Ken
Hatano, Naomichi
Feinberg, Joshua
Obuse, Hideaki
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2005_02705
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
Mochizuki, Ken
Hatano, Naomichi
Feinberg, Joshua
Obuse, Hideaki
Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
Quantum Physics
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.
title Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
topic Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
Quantum Physics
url https://arxiv.org/abs/2005.02705