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Published November 16, 2021 | Submitted + Published
Journal Article Open

Emergent Replica Conformal Symmetry in Non-Hermitian SYK₂ Chains

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-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) O(2)×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∼ρ_s log L_A, where ρ_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.

Additional Information

© 2021. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Published: 2021-11-16. We acknowledge helpful discussions with Ehud Altman. PZ acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. SKJ is supported by the Simons Foundation via the It From Qubit Collaboration. CL is supported by the NSF CMMT program under Grants No. DMR-1818533. Use was made of computational facilities purchased with funds from the National Science Foundation (CNS-1725797) and administered by the Center for Scientific Computing (CSC). The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center (MRSEC; NSF DMR-1720256) at UC Santa Barbara.

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Published - q-2021-11-16-579.pdf

Submitted - 2104.04088.pdf

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Additional details

Created:
August 20, 2023
Modified:
October 23, 2023