Symmetry-resolved entanglement in critical non-Hermitian systems

• URL: http://arxiv.org/abs/2303.05232v2
• Date: Wed, 31 May 2023 16:36:10 GMT
• Title: Symmetry-resolved entanglement in critical non-Hermitian systems
• Authors: Michele Fossati, Filiberto Ares, Pasquale Calabrese
• Abstract summary: We study the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $rho_A$ and $|rho_A|$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The study of entanglement in the symmetry sectors of a theory has recently attracted a lot of attention since it provides better understanding of some aspects of quantum many-body systems. In this paper, we extend this analysis to the case of non-Hermitian models, in which the reduced density matrix $\rho_A$ may be non-positive definite and the entanglement entropy negative or even complex. Here we examine in detail the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point, a model that preserves particle number and whose scaling limit is a $bc$-ghost non-unitary CFT. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $\rho_A$ and $|\rho_A|$. From them, we can understand the origin of the non-positiveness of $\rho_A$ and naturally define a positive-definite reduced density matrix in each charge sector, which gives a well-defined symmetry-resolved entanglement entropy. As byproduct, we also obtain the analytical distribution of the critical entanglement spectrum.

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