Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories

TL;DR

This paper introduces a biorthogonal basis method to analyze entanglement in non-Hermitian topological systems, revealing topological features and critical behavior linked to non-unitary conformal field theories.

Contribution

It presents a novel approach for computing entanglement in non-Hermitian systems and connects entanglement properties to topological and conformal field theory aspects.

Findings

Entanglement spectrum reveals topological mid-gap states.

At criticality, entanglement entropy scales logarithmically with central charge -2.

Identifies a non-unitary conformal field theory in a non-Hermitian lattice model.

Abstract

We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) and the non-Hermitian Chern insulators. In addition, we find that at a critical point in the PT symmetric SSH model, the entanglement entropy has a logarithmic scaling with corresponding central charge $c=-2$. This critical point then is a free-fermion lattice realization of the non-unitary conformal field theory.