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Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics

Zhang, Pengfei and Liu, Chunxiao and Jian, Shao-Kai and Chen, Xiao (2022) Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics. Quantum, 6 . Art. No. 723. ISSN 2521-327X. doi:10.22331/q-2022-05-27-723.

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Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand the effect of long-range hopping that decays with r^(−α) in non-Hermitian free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-N SYK₂ chain and a single-flavor fermion chain and we show that they share the same phase diagram. When α > 0.5, we observe two critical phases with subvolume entanglement scaling: (i) α > 1.5, a logarithmic phase with dynamical exponent z = 1 and logarithmic subsystem entanglement, and (ii) 0.5 < α < 1.5, a fractal phase with z = 2α−1/2 and subsystem entanglement S_A∝L^(1−z)/A, where L_A is the length of the subsystem A. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as L/T. We then confirm that the results are also valid for the static SYK₂ chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurement-induced phase transitions.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Zhang, Pengfei0000-0002-7408-0918
Liu, Chunxiao0000-0002-0695-1291
Jian, Shao-Kai0000-0003-3058-8725
Additional Information: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: 2022-05-27. 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.
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
Record Number:CaltechAUTHORS:20210629-200841842
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109652
Deposited By: Tony Diaz
Deposited On:29 Jun 2021 22:35
Last Modified:11 Jul 2022 21:58

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