Renyi Entropy Measures for Quantum Entanglement Characterization

P. K. Aravind

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

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 Rényi 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 Rényi 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/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.

John Cardy

Jesse C. Cresswell

Recently it was shown that the growth of entanglement in an initially separable state, as measured by the purity of subsystems, can be characterized by a timescale that takes a universal form for any Hamiltonian. We show that the same timescale governs the growth of entanglement for all R\'enyi entropies. Since the family of R\'enyi entropies completely characterizes the entanglement of a pure bipartite state, our timescale is a universal feature of bipartite entanglement. The timescale depends only on the interaction Hamiltonian and the initial state.

Surajit Bera, Arijit Haldar, Sumilan Banerjee

Quantum entanglement, lacking any classical counterpart, provides a fundamental new route to characterize the quantum nature of many-body states. In this work, we discuss an implementation of a new path integral method [Phys. Rev. Res. 2, 033505 (2020)] for fermions to compute entanglement for extended subsystems in the Hubbard model within dynamical mean-field theory (DMFT) in one and two dimensions. The new path integral formulation measures entanglement by applying a ``kick'' to the underlying interacting fermions. We show that the R\'enyi entanglement entropy can be extracted efficiently within the DMFT framework by integrating over the strength of the kick term. Using this method, we compute the second R\'enyi entropy as a function of subsystem size for metallic and Mott insulating phases of the Hubbard model. We explore the thermal entropy to entanglement crossover in the subsystem R\'enyi entropy in the correlated metallic phase. We show that the subsystem-size scaling of the second R\'enyi entropy is well described by the crossover formula which interpolates between the volume-law thermal R\'enyi entropy and the universal boundary-law R\'enyi entanglement entropy with logarithmic violation, as predicted by conformal field theory. We also study the mutual information across the Mott metal-insulator transition.

Xue Yang, Yanhan Yang, Zhao Li-ming +1 more