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

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 Renyi 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 Renyi 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/Renyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/Renyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic n-th Renyi entropy captures the expected entanglement property, whereas the traditional Renyi entropy can exhibit unnatural singularities due to its improper definition.