# Rényi entropies and negative central charges in non-Hermitian quantum systems

### Submission summary

 As Contributors: Po-Yao Chang Arxiv Link: https://arxiv.org/abs/2107.13006v6 (pdf) Date accepted: 2022-06-01 Date submitted: 2022-05-20 04:50 Submitted by: Chang, Po-Yao Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approaches: Theoretical, Computational

### 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.

Published as SciPost Phys. 12, 194 (2022)

We thank the Referee for the suggestion and we follow the suggestion accordingly.

### List of changes

In Sec. 2.2, we add the discussion regarding to the XXZ model and the complex-weight six-vertex model which the central charge c=1-6 \frac{\theta^2/\pi^2}{1- \theta / \pi}.

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 194 (2022)

Resubmission 2107.13006v6 on 20 May 2022
Resubmission 2107.13006v5 on 3 May 2022
Submission 2107.13006v4 on 17 March 2022

## Reports on this Submission

### Report

The authors have implemented the requested changes. I recommend this manuscript for publication.

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