Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 340, Issue 2, Pages 499-561Publisher
SPRINGER
DOI: 10.1007/s00220-015-2473-y
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Funding
- Government of Canada through NSERC
- Province of Ontario through MRI
- EU ERC Advanced Grant NLST [PHYS RQ8784]
- EU Qessence project
- EPSRC
- Templeton Foundation
- COST Action [MP1209]
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It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work, we give rigorous analytic results on thermalization for translation-invariant quantum lattice systems with finite-range interaction of arbitrary strength, in all cases where there is a unique equilibrium state at the corresponding temperature. We clarify the physical picture by showing that subsystems relax towards the reduction of the global Gibbs state, not the local Gibbs state, if the initial state has close to maximal population entropy and certain non-degeneracy conditions on the spectrumare satisfied.Moreover,we showthat almost all pure states with support on a small energy window are locally thermal in the sense of canonical typicality. We derive our results from a statement on equivalence of ensembles, generalizing earlier results by Lima, and give numerical and analytic finite size bounds, relating the Ising model to the finite de Finetti theorem. Furthermore, we prove that global energy eigenstates are locally close to diagonal in the local energy eigenbasis, which constitutes a part of the eigenstate thermalization hypothesis that is valid regardless of the integrability of the model.
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