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 nonpositive 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 nonunitary conformal field theory (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 nonpositiveness 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 a by-product, we also obtain the analytical distribution of the critical entanglement spectrum.

Symmetry-resolved entanglement in critical non-Hermitian systems / Fossati, Michele; Ares, Filiberto; Calabrese, Pasquale. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 107:20(2023). [10.1103/PhysRevB.107.205153]

Symmetry-resolved entanglement in critical non-Hermitian systems

Fossati, Michele;Ares, Filiberto;Calabrese, Pasquale
2023-01-01

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 nonpositive 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 nonunitary conformal field theory (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 nonpositiveness 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 a by-product, we also obtain the analytical distribution of the critical entanglement spectrum.
2023
107
20
205153
https://arxiv.org/abs/2303.05232
Fossati, Michele; Ares, Filiberto; Calabrese, Pasquale
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/136497
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