Exact solution of the relationship between the eigenvalue discreteness and the behavior of eigenstates in Su-Schrieffer-Heeger lattices

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Wei, Huitong, Wang, Xiumei, Zhou, Xingping
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866929706072276992
author Wei, Huitong
Wang, Xiumei
Zhou, Xingping
author_facet Wei, Huitong
Wang, Xiumei
Zhou, Xingping
contents Eigenstate localization and bulk-boundary correspondence are fundamental phenomena in one-dimensional (1D) Su-Schrieffer-Heeger (SSH) lattices. The eigenvalues discreteness and the eigenstates localization exhibit a high degree of consistency as system information evolve. We explore the relationship between the eigenvalue discreteness and the eigenstates behavior in 1D SSH lattices. The discreteness fraction and the inverse participation ratio (IPR) combined with a Taylor expansion are utilized to describe the relationship. In the Hermitian case, we employ the bulk-edge correspondence and the perturbation theory to derive an exact solution considering both zero and non-zero modes. We also extend our analysis to the non-Hermitian cases, assuming that eigenvalues remain purely real. Our findings reveal a logarithmic relationship between the degree of eigenvalue discreteness and eigenstates localization, which holds under both the Hermitian and non-Hermitian conditions. This result is fully consistent with the theoretical predictions.
format Preprint
id arxiv_https___arxiv_org_abs_2502_05865
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Exact solution of the relationship between the eigenvalue discreteness and the behavior of eigenstates in Su-Schrieffer-Heeger lattices
Wei, Huitong
Wang, Xiumei
Zhou, Xingping
Other Condensed Matter
Eigenstate localization and bulk-boundary correspondence are fundamental phenomena in one-dimensional (1D) Su-Schrieffer-Heeger (SSH) lattices. The eigenvalues discreteness and the eigenstates localization exhibit a high degree of consistency as system information evolve. We explore the relationship between the eigenvalue discreteness and the eigenstates behavior in 1D SSH lattices. The discreteness fraction and the inverse participation ratio (IPR) combined with a Taylor expansion are utilized to describe the relationship. In the Hermitian case, we employ the bulk-edge correspondence and the perturbation theory to derive an exact solution considering both zero and non-zero modes. We also extend our analysis to the non-Hermitian cases, assuming that eigenvalues remain purely real. Our findings reveal a logarithmic relationship between the degree of eigenvalue discreteness and eigenstates localization, which holds under both the Hermitian and non-Hermitian conditions. This result is fully consistent with the theoretical predictions.
title Exact solution of the relationship between the eigenvalue discreteness and the behavior of eigenstates in Su-Schrieffer-Heeger lattices
topic Other Condensed Matter
url https://arxiv.org/abs/2502.05865