Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

TL;DR

This paper investigates the entanglement spectrum in non-Hermitian fermionic systems, revealing how it encodes topological properties and symmetries, with differences depending on the choice of eigenstates and phase types.

Contribution

It introduces a framework for analyzing the entanglement spectrum in non-Hermitian models, highlighting how biorthogonal approaches reflect topological features and symmetry mappings.

Findings

Entanglement spectra can be computed efficiently in non-Hermitian systems.

Biorthogonal entanglement Hamiltonian inherits topological properties in line gapped phases.

Distinct information is carried by right and left density matrices regarding topological features.

Abstract

We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.