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Emergent Replica Conformal Symmetry in Non-Hermitian SYK₂ Chains

Zhang, Pengfei and Jian, Shao-Kai and Liu, Chunxiao and Chen, Xiao (2021) Emergent Replica Conformal Symmetry in Non-Hermitian SYK₂ Chains. Quantum, 5 . Art. No. 579. ISSN 2521-327X. doi:10.22331/q-2021-11-16-579.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Zhang, Pengfei0000-0002-7408-0918
Alternate Title:SYK Meets Non-Hermiticity I: Emergent Replica Conformal Symmetry, Emergent Replica Conformal Symmetry in Non-Hermitian SYK2 Chains
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.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
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Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Simons FoundationUNSPECIFIED
California NanoSystems InstituteUNSPECIFIED
Record Number:CaltechAUTHORS:20210413-083455122
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108710
Deposited By: Tony Diaz
Deposited On:13 Apr 2021 21:46
Last Modified:04 Jan 2022 21:27

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