Quasi-Hermitian extended SSH models

TL;DR

This paper explores the quasi-Hermitian limit of a non-Hermitian extended SSH model, revealing how real spectra and edge states can be characterized using modified topological invariants, even when the quasi-Hermitian condition is violated.

Contribution

It introduces a framework for analyzing the topological properties of quasi-Hermitian non-Hermitian models and extends the criteria to cases beyond the quasi-Hermitian condition.

Findings

Real energy spectra in the quasi-Hermitian limit

Modified bulk-boundary correspondence using winding numbers

No inconsistencies found when extending criteria beyond quasi-Hermitian conditions

Abstract

We consider the quasi Hermitian limit of a non-Hermitian extended Su Schrieffer Heeger model, in which the hopping amplitudes obey a specific relation so that the system may be mapped to a corresponding Hermitian one and its energy spectrum is completely real. Analogous to the Hermitian case, one may use the modified winding number to determine the total number of edge states on the boundaries to achieve a modified bulk-boundary correspondence. Due to the skin effect in nonHermitian systems, the spectral winding numbers must be used to classify such systems further. It dictates how the edge states would be distributed over the left and right boundaries. We then naively extend the criteria to the cases that the quasi Hermitian condition is violated. For all the cases that we consider, no inconsistency has been found.