Random matrix theory for quantum and classical metastability in local Liouvillians

Li, Jimin L; Rose, Dominic C; Garrahan, Juan P.; Luitz, David J

Abstract

We consider the effects of strong dissipation in quantum systems with a notion of locality, which induces a hierarchy of many-body relaxation timescales as shown in [Phys. Rev. Lett. 124, 100604 (2020)]. If the strength of the dissipation varies strongly in the system, additional separations of timescales can emerge, inducing a manifold of metastable states, to which observables relax first, before relaxing to the steady state. Our simple model, involving one or two "good" qubits with dissipation reduced by a factor α < 1 compared to the other "bad" qubits, confirms this picture and admits a perturbative treatment. Introduction-Quantum many-body systems are generically complex, and obtaining an analytic understanding of the position of all spectral resonances is often hopeless. It was realized early on [1-6] that this complexity is in fact so great that many statistical properties of the spectrum are identical with those of random matrices sampled from an ensemble determined by the symmetry of the system. These pioneering observations have been subsequently refined, resulting in cornerstones of our understanding of thermalization in unitary quantum many-body systems by virtue of the eigenstate thermalization hypothesis [7-14], only with exceptions in integrable [15-18], many-body localized [19-29], time-crystalline [30-32] or scarred and constrained systems [33-35].

• Journal Article Type: Article
• Acceptance Date: Apr 20, 2022
• Online Publication Date: May 6, 2022
• Publication Date: May 1, 2022
• Deposit Date: Apr 21, 2022
• Publicly Available Date: May 1, 2022
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society (APS)
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 18
• Article Number: L180201
• DOI: https://doi.org/10.1103/physrevb.105.l180201
• Public URL: https://nottingham-repository.worktribe.com/output/7784336
• Publisher URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.L180201
• Additional Information: ©2022 American Physical Society