Rapid thermalization of spin chain commuting Hamiltonians

• URL: http://arxiv.org/abs/2112.00593v2
• Date: Tue, 11 Jan 2022 16:09:18 GMT
• Title: Rapid thermalization of spin chain commuting Hamiltonians
• Authors: Ivan Bardet, \'Angela Capel, Li Gao, Angelo Lucia, David P\'erez-Garc\'ia and Cambyse Rouz\'e
• Abstract summary: We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.
• Score: 13.349045680843885
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians, reaching equilibrium in a time which scales logarithmically with the system size. Our main result is a generalization to the quantum setting of a seminal result of Holley and Stroock for classical spin chains and represents an exponential improvement over bounds based on the non-closure of the spectral gap. From a physical point of view, our result rigorously establishes the absence of dissipative phase transition for Davies evolutions over translation-invariant spin chains. The result also applies in the case of Symmetry Protected Topological phases where the evolution is respecting the symmetry of the phase. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.

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