The topological counterparts of non-Hermitian SSH models

TL;DR

This paper introduces a method to construct topological equivalent models of non-Hermitian SSH systems using similarity transformations, enabling analytic calculation of topological invariants despite the non-Hermitian skin effect.

Contribution

It proposes a novel approach to analyze non-Hermitian topological models by transforming them into equivalent Hermitian-like models, simplifying the study of their topological properties.

Findings

Successfully applied to various non-Hermitian SSH models

Allows analytic computation of topological invariants

Provides an alternative framework for non-Hermitian topological analysis

Abstract

The breakdown of the conventional bulk-boundary correspondence due to non-Hermitian skin effect leads to the non-Bloch bulk-boundary correspondence in the generalized Brillouin zone. Inspired by the case of the equivalence between the non-reciprocal hopping and imaginary gauge field, we propose a method to construct the topological equivalent models of the non-Hermitian dimerized lattices with the similarity transformations. The idea of the constructions is from that the imaginary magnetic flux vanishes under the open boundary condition and the period boundary spectra can be well approximated by open boundary spectra. As an illustration, we apply this approach to several representative non-Hermitian SSH models, efficiently obtaining topological invariants in analytic form defined in the conventional Bloch bands. The method gives an alternative way to study the topological properties of non-Hermitian system.