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Journal Articles Physical Review Letters Year : 2023

Rapid thermalization of spin chain commuting Hamiltonians


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.

Dates and versions

hal-03538313 , version 1 (21-01-2022)




Ivan Bardet, Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, et al.. Rapid thermalization of spin chain commuting Hamiltonians. Physical Review Letters, 2023, 130 (6), pp.8. ⟨10.1103/PhysRevLett.130.060401⟩. ⟨hal-03538313⟩
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