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

by Yi-Ting Tu, Yu-Chin Tzeng, Po-Yao Chang

This Submission thread is now published as SciPost Phys. 12, 194 (2022)

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)



Author comments upon resubmission

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}.


Reports on this Submission

Anonymous Report 1 on 2022-5-20 (Invited Report)

Report

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

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