Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders

TL;DR

This paper analytically explores the entanglement Hamiltonian and energy spectrum of non-Hermitian quantum spin ladders, revealing how entanglement properties relate to effective temperature and coupling in these systems.

Contribution

It introduces a perturbative approach to analyze entanglement in non-Hermitian spin ladders, showing the entanglement Hamiltonian resembles a single-chain Hamiltonian with renormalized couplings.

Findings

Entanglement Hamiltonian approximates a single-chain Hamiltonian in strong coupling.

An effective temperature can be defined from the entanglement spectrum.

Provides a basis for studying finite temperature effects in non-Hermitian systems.

Abstract

Quantum entanglement plays a crucial role not only in understanding Hermitian many-body systems but also in offering valuable insights into non-Hermitian quantum systems. In this paper, we analytically investigate the entanglement Hamiltonian and entanglement energy spectrum of a non-Hermitian spin ladder using perturbation theory in the biorthogonal basis. Specifically, we examine the entanglement properties between coupled non-Hermitian quantum spin chains. In the strong coupling limit ($J_\mathrm{rung}\gg1$), first-order perturbation theory reveals that the entanglement Hamiltonian closely resembles the single-chain Hamiltonian with renormalized coupling strengths, allowing for the definition of an ad hoc temperature. Our findings provide new insights into quantum entanglement in non-Hermitian systems and offer a foundation for developing novel approaches for studying finite temperature properties in non-Hermitian quantum many-body systems.