Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy

TL;DR

This paper investigates the topological phases of one-dimensional non-Hermitian systems using edge entanglement entropy, revealing how interactions influence the bulk-boundary correspondence.

Contribution

It introduces edge entanglement entropy as a tool to characterize topological phases in non-Hermitian systems, including interacting Hubbard chains, and maps the phase diagram.

Findings

Edge entanglement entropy effectively distinguishes phases in non-Hermitian systems.

Hubbard interaction reduces the breakdown of bulk-boundary correspondence.

Critical interaction strength restores the bulk-boundary correspondence.

Abstract

Dramatically different from the Hermitian systems, the conventional Bulk-Boundary Correspondence (BBC) is broken in the non-Hermitian systems. In this article, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free Fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain, and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of Bulk-Boundary Correspondence, which eventually disappears at some critical value of interaction.