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Krylov complexity as a probe of the quantum Mpemba effect

Mohsen Alishahiha* and Mohammad Javad Vasli†

  • *Contact author: alishah@ipm.ir
  • †Contact author: vasli@ipm.ir
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Phys. Rev. D 113, 045004 – Published 4 February, 2026

DOI: https://doi.org/10.1103/7wkj-w8c9

Abstract

We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global U(1) symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional diagnostics such as the trace distance, while offering a complementary interpretation in terms of Hilbert-space exploration and dynamical delocalization. In U(1)-symmetric systems, we confirm that the recently proposed symmetric component of Krylov complexity serves as a robust and reliable indicator of the quantum Mpemba effect, capturing anomalous relaxation even in cases where the total complexity fails to do so.

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Phys. Rev. D 113, 045004– Published 4 February, 2026
  • Received 31 October 2025
  • Accepted 24 December 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. Funded by SCOAP3.

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