Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains

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 quadrati...

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Autores principales:	Pengfei Zhang, Shao-Kai Jian, Chunxiao Liu, Xiao Chen
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/fe00f8683fad4b4fb9cfb6bb7b28207f
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spelling	oai:doaj.org-article:fe00f8683fad4b4fb9cfb6bb7b28207f2021-11-16T12:16:53ZEmergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains2521-327X10.22331/q-2021-11-16-579https://doaj.org/article/fe00f8683fad4b4fb9cfb6bb7b28207f2021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-16-579/pdf/https://doaj.org/toc/2521-327XRecently, 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) ${O(2)\times O(2)}$ 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 ${S\sim \rho_s \log L_A}$, 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.Pengfei ZhangShao-Kai JianChunxiao LiuXiao ChenVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 579 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Pengfei Zhang Shao-Kai Jian Chunxiao Liu Xiao Chen Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains
description	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) ${O(2)\times O(2)}$ 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 ${S\sim \rho_s \log L_A}$, 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.
format	article
author	Pengfei Zhang Shao-Kai Jian Chunxiao Liu Xiao Chen
author_facet	Pengfei Zhang Shao-Kai Jian Chunxiao Liu Xiao Chen
author_sort	Pengfei Zhang
title	Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains
title_short	Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains
title_full	Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains
title_fullStr	Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains
title_full_unstemmed	Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains
title_sort	emergent replica conformal symmetry in non-hermitian syk$_2$ chains
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/fe00f8683fad4b4fb9cfb6bb7b28207f
work_keys_str_mv	AT pengfeizhang emergentreplicaconformalsymmetryinnonhermitiansyk2chains AT shaokaijian emergentreplicaconformalsymmetryinnonhermitiansyk2chains AT chunxiaoliu emergentreplicaconformalsymmetryinnonhermitiansyk2chains AT xiaochen emergentreplicaconformalsymmetryinnonhermitiansyk2chains
_version_	1718426582927802368

Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains

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