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Emergent Replica Conformal Symmetry in Non-Hermitian SYK2 Chains

TitleEmergent Replica Conformal Symmetry in Non-Hermitian SYK2 Chains
Publication TypeJournal Article
Year of Publication2021
AuthorsP. Zhang, S-K. Jian, C. Liu, and X. Chen
JournalQuantum
Volume5
Date PublishedNOV 16
Type of ArticleArticle
ISSN2521-327X
Abstract

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-YeKitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) O(2) x O(2) symmetries, which is broken to O(2) by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem A with length L-A corresponds to the energy of the half-vortex pair S similar to rho(s) log L-A, where rho(s) is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.