Entanglement Hamiltonian in the non-Hermitian SSH model

TL;DR

This paper investigates the entanglement Hamiltonian in the non-Hermitian SSH model, revealing a lattice Bisognano-Wichmann structure in the gapped phase and a novel imaginary chemical potential at criticality, explaining negative entanglement entropy.

Contribution

It extends the understanding of entanglement Hamiltonians to non-Hermitian systems, identifying new features at criticality not present in Hermitian models.

Findings

Entanglement Hamiltonian in the gapped phase aligns with lattice Bisognano-Wichmann theorem.

Discovery of a new imaginary chemical potential term at criticality.

Negative entanglement entropy observed at the critical point.

Abstract

Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.