Random matrix theory for quantum and classical metastability in local Liouvillians

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 $\alpha <1$ compared to the other "bad" qubits, confirms this picture and admits a perturbative treatment.

5 pages, 3 figures plus supplementary material

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• Spectral and steady-state properties of fermionic random quadratic Liouvillians
• Compressed quantum error mitigation
• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study