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Quantum thermalization mechanism and the emergence of symmetry-breaking phases

Sebastián Gómez1,2,*, Ángel L. Corps3,4,†, and Armando Relaño1,4,‡

  • 1Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
  • 2Instituto de Estructura de la Materia, IEM-CSIC, Serrano 123, E-28006 Madrid, Spain
  • 3Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague, Czech Republic
  • 4Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain

  • *Contact author: sebastian.gomez@csic.es
  • †Contact author: corps.angel.l@gmail.com
  • ‡Contact author: armando.relano@fis.ucm.es
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APS Open Sci. 1, 000018 – Published 8 May, 2026

DOI: https://doi.org/10.1103/w77n-lyjd

Abstract

We propose a generalization of the eigenstate thermalization hypothesis accountin g for the emergence of symmetry-breaking phases. It consists of two conditions that any system with a degenerate spectrum must fulfill in order to thermalize. The failure of each condition generates a different nonthermalizing scenario. One is due to the absence of chaos and may indicate that extra constants of motion are required to describe equilibrium states. The other one implies the existence of initial conditions evolving toward symmetry-breaking equilibrium states. If it spreads across an entire spectral region, then this region gives rise to a symmetry-breaking phase. We explore the applicability of this formalism by means of numerical experiments on a three-site Bose-Hubbard model with two noncommuting discrete symmetries.

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APS Open Sci. 1, 000018– Published 8 May, 2026
Vol. 1
  • Received 29 August 2025
  • Revised 1 December 2025
  • Accepted 1 May 2026
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