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SYK Meets Non-Hermiticity I: Emergent Replica Conformal Symmetry

Zhang, Pengfei and Jian, Shao-Kai and Liu, Chunxiao and Chen, Xiao (2021) SYK Meets Non-Hermiticity I: Emergent Replica Conformal Symmetry. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210413-083455122

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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 their 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 stiffness of the Goldstone mode. We also discuss special limits where more than one Goldstone mode exists and comment on interaction effects.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2104.04088arXivDiscussion Paper
ORCID:
AuthorORCID
Zhang, Pengfei0000-0002-7408-0918
Additional Information:Attribution 4.0 International (CC BY 4.0). 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.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Simons FoundationUNSPECIFIED
NSFDMR-1818533
NSFCNS-1725797
California NanoSystems InstituteUNSPECIFIED
NSFDMR-1720256
Record Number:CaltechAUTHORS:20210413-083455122
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210413-083455122
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108710
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Apr 2021 21:46
Last Modified:13 Apr 2021 21:46

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