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

Yi-Ting Tu¹, Yu-Chin Tzeng^2*, Po-Yao Chang²

¹Department of Physics, University of Maryland, College Park, MD, USA
²Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Yu-Chin Tzeng, email:yctzeng@mx.nthu.edu.tw

Quantum entanglement is one essential element to characterize many-body quantum systems. However, so far, the entanglement measures mainly restrict to Hermitian systems. Here, we propose a natural extension of entanglement and Rényi entropies to non-Hermitian quantum systems. We demonstrate the generic entanglement and Rényi entropies capture the correct 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/Rényi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/Rényi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic n-th Rényi entropy captures the expected entanglement property, whereas the traditional Rényi entropy can exhibit unnatural singularities due to its improper definition.
[1] Y.-T. Tu, Y.-C. Tzeng, and P.-Y. Chang, Rényi entropies and negative central charges in non-Hermitian quantum systems, arXiv:2107.13006
[2] Y.-C. Tzeng, C.-Y. Ju, G.-Y. Chen, and W.-M. Huang, Hunting for the non-Hermitian exceptional points with fidelity susceptibility, Phys. Rev. Research 3, 013015 (2021)

Keywords: non-Hermitian, entanglement, quantum phase transition, central charge, exact diagonalization