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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