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Temperature and conditions for thermalization after canonical quenches

Lennart Dabelow*

  • *Contact author: l.dabelow@qmul.ac.uk
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Phys. Rev. B 112, 184307 – Published 12 November, 2025

DOI: https://doi.org/10.1103/bp6q-ydvv

Abstract

We consider quenches of a quantum system that is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. Technically, our main result is a systematic expansion of the pre- and postquench canonical ensembles in the quench strength. We first demonstrate how this can be used to predict the system's temperature after the quench from equilibrium properties at the prequench temperature. For a thermalizing postquench system, it furthermore allows us to calculate equilibrium observable expectation values. Finally, in the presence of additional conserved quantities besides the Hamiltonian, we obtain a hierarchy of necessary conditions for thermalization towards the (postquench) canonical ensemble. At first order, these thermalization conditions have a nice geometric interpretation in operator space with the canonical covariance as a semi-inner product: The quench operator (difference between post- and prequench Hamiltonians) and the conserved quantity must be orthogonal in the orthogonal complement of the postquench Hamiltonian. We illustrate the results numerically for a variety of setups involving integrable and nonintegrable models.

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Phys. Rev. B 112, 184307– Published 12 November, 2025
  • Received 25 June 2025
  • Revised 18 September 2025
  • Accepted 27 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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