R\'enyi entropies and negative central charges in non-Hermitian quantum systems

TL;DR

This paper extends entanglement and Re9nyi entropies to non-Hermitian quantum systems, demonstrating their effectiveness in capturing entanglement properties and negative central charges in non-unitary conformal field theories.

Contribution

It introduces a new definition of entanglement and Re9nyi entropies for non-Hermitian systems, aligning with non-unitary CFT predictions and improving analysis of topological phases.

Findings

Excellent agreement with non-unitary CFT predictions of negative central charges.

The generic Re9nyi entropy accurately captures entanglement in non-Hermitian topological phases.

Traditional Re9nyi entropy can show unnatural singularities, unlike the proposed definition.

Abstract

Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi entropies to non-Hermitian quantum systems. There have been other proposals for the computation of these quantities, which are distinct from what is proposed in the current paper. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and R\'enyi entropies. These quantities capture the desired entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/R\'enyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/R\'enyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic $n$-th R\'enyi entropy captures the expected entanglement property, whereas the traditional R\'enyi entropy can exhibit unnatural singularities due to its improper definition.