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  • Open Access

Floquet Thermalization via Instantons near Dynamical Freezing

Rohit Mukherjee*,†, Haoyu Guo*, and Debanjan Chowdhury‡

  • *These authors contributed equally to this work.
  • †Present address: Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany.
  • ‡Contact author: debanjanchowdhury@cornell.edu
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Phys. Rev. X 16, 011041 – Published 27 February, 2026

DOI: https://doi.org/10.1103/4w5w-57my

Abstract

Periodically driven Floquet quantum many-body systems have revealed new insights into the rich interplay of thermalization and growth of entanglement. The phenomenology of dynamical freezing, whereby a translationally invariant many-body system exhibits emergent conservation laws and a slow growth of entanglement entropy at certain fixed ratios of a drive amplitude and frequency, presents a novel paradigm for retaining memory of an initial state up to late times. Previous studies of dynamical freezing have largely been restricted to a high-frequency Floquet-Magnus expansion and numerical exact diagonalization. Both techniques are unable to capture the slow approach to thermalization, or lack thereof, in a systematic fashion. By employing Floquet flow renormalization, where the time-dependent part of the Hamiltonian is gradually decoupled from the effective Hamiltonian using a sequence of unitary transformations, we unveil the universal approach to dynamical freezing and beyond, at asymptotically late times. We analyze the fixed-point behavior associated with the flow renormalization at and near freezing using both exact-diagonalization and tensor-network-based methods and contrast the results with the conventional prethermal phenomenon. For a generic nonintegrable spin Hamiltonian with a periodic cosine wave drive, the flow approaches an unstable fixed point with an approximate emergent symmetry. We observe that at freezing the thermalization timescales are delayed compared to away from freezing, and the flow trajectory undergoes a series of instanton events. Our numerical results are supported by analytical solutions to the flow equations.

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Popular Summary

Periodically driven quantum many-body systems typically heat up rapidly to a featureless, infinite-temperature state, yet they can sometimes exhibit dynamical freezing where memory of an initial state is retained for unexpectedly long intervals. We employ a nonperturbative Floquet flow-renormalization framework to reveal that this frozen state is eventually punctured by sudden, rare tunneling events known as instantons. These instanton events connect a sequence of intermediate unstable fixed points, disrupting emergent conservation laws and initiating the slow but inevitable approach to thermal equilibrium. Our analysis demonstrates that while freezing slows thermalization, the phenomenon is asymptotic and subject to a nontrivial interplay between drive frequency and system size. Broadly, these findings provide a universal physical picture of how periodically driven systems escape ergodicity breaking, offering new strategies for controlling heating in many-body quantum devices.

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Phys. Rev. X 16, 011041– Published 27 February, 2026
  • Received 1 January 2025
  • Revised 16 December 2025
  • Accepted 28 January 2026
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