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  • Letter
  • Open Access

Translation symmetry restoration in integrable systems: The noninteracting case

Molly Gibbins1,2, Adam Gammon-Smith1,2, and Bruno Bertini3

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Phys. Rev. B 112, L180307 – Published 21 November, 2025

DOI: https://doi.org/10.1103/mxhd-fswm

Abstract

The study of symmetry restoration has recently emerged as a fruitful means to extract high-level information on the relaxation of quantum many-body systems. However, while the restoration of internal symmetries has been investigated intensively, that of spatial symmetries has hitherto only been considered in the context of random unitary circuits. Here, we present a complementary study of translation symmetry restoration in integrable systems. In particular, we consider a one-dimensional chain of spinless, noninteracting fermions quenched from a ν>1 shift invariant state, and follow the local restoration of one-site shift invariance using the Frobenius distance ΔFA between the state on a subsystem and its symmetrized counterpart. Distinct from the case of random unitary circuits, where symmetry restoration occurs abruptly for times proportional to the subsystem size, we find that symmetry here is restored smoothly and over timescales of the order of the subsystem size squared. We also find that the so-called ‘‘quantum Mpemba effect’’ is readily observed. Most importantly, we show that—in contrast to the case of continuous internal symmetries—this discrete symmetry restoration is not qualitatively described by a quasiparticle picture for ΔFA, and therefore goes beyond the hydrodynamic description. Our results can be directly extended to higher dimensions.

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References (38)

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Phys. Rev. B 112, L180307– Published 21 November, 2025
  • Received 30 June 2025
  • Revised 17 October 2025
  • Accepted 21 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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