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Basis dependence of eigenstate thermalization

Lennart Dabelow1, Christian Eidecker-Dunkel2, and Peter Reimann2

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Phys. Rev. B 113, 094311 – Published 23 March, 2026

DOI: https://doi.org/10.1103/znfb-96vf

Abstract

Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. In systems with degeneracies, the choice of an energy eigenbasis is not unique and the fraction of basis states exhibiting eigenstate thermalization can vary. We present a simple example where this fraction vanishes in the thermodynamic limit for one basis choice, but remains nonzero for another choice. In other words, the weak eigenstate thermalization hypothesis is satisfied in the first, but violated in the second basis. We furthermore prove that degeneracies must abound whenever a system is simultaneously symmetric under spatial translations and reflection. Finally, we derive general bounds on how strongly eigenstate thermalization may depend on the choice of the basis, and we reveal some interesting implications regarding the temporal relaxation properties of such systems.

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Phys. Rev. B 113, 094311– Published 23 March, 2026
  • Received 29 July 2025
  • Revised 17 November 2025
  • Accepted 2 March 2026
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