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Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model

Jian, Shao-Kai and Liu, Chunxiao and Chen, Xiao and Swingle, Brian and Zhang, Pengfei (2021) Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model. Physical Review Letters, 127 (14). Art. No. 140601. ISSN 0031-9007. doi:10.1103/PhysRevLett.127.140601.

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We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-N limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK₂ chains, the model features a continuous O(2) symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous O(2) symmetry is explicitly lowered to a discrete C₄ symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by C₄ symmetry breaking. We also verify the large-N critical exponents by numerically solving the Schwinger-Dyson equation.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Jian, Shao-Kai0000-0003-3058-8725
Liu, Chunxiao0000-0002-0695-1291
Swingle, Brian0000-0003-0334-3108
Zhang, Pengfei0000-0002-7408-0918
Alternate Title:Quantum error as an emergent magnetic field
Additional Information:© 2021 American Physical Society. Received 28 April 2021; revised 30 July 2021; accepted 17 August 2021; published 27 September 2021. We acknowledge helpful discussions with Ehud Altman, Yimu Bao, Subhayan Sahu, and Greg Bentsen. S. K. J. and B. G. S. are supported by the Simons Foundation via the It From Qubit Collaboration. The work of B. G. S. is also supported in part by the AFOSR under Grant No. FA9550-19-1-0360. C. L. is supported by the NSF CMMT program under Grants No. DMR-1818533. P. Z. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. We acknowledge the University of Maryland High Performance Computing Cluster (HPCC).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0360
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Issue or Number:14
Record Number:CaltechAUTHORS:20211004-232846320
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111212
Deposited By: George Porter
Deposited On:08 Oct 2021 20:12
Last Modified:13 Oct 2021 20:50

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