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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 (2021) Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics. 11. . (Unpublished)

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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 its interplay with long-range hopping that decays with r^(−α) in 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:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Zhang, Pengfei0000-0002-7408-0918
Additional Information:Attribution 4.0 International (CC BY 4.0). 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
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:11
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:29 Jun 2021 22:35

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