Symmetry-resolved entanglement in critical non-Hermitian systems

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.

19 pages, 5 figures. Minor clarifications, typos corrected . Final version published in Phys. Rev. B

References in corpus (14)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Entanglement negativity in quantum field theory
• Topological Transition in a Non-Hermitian Quantum Walk
• Entanglement spectrum in one-dimensional systems
• Topological invariance and global Berry phase in non-Hermitian systems
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Entanglement equipartition in critical random spin chains
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Negativity spectrum of one-dimensional conformal field theories
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Equipartition of Entanglement in Quantum Hall States