On Krylov Complexity as a Probe of the Quantum Mpemba Effect

• URL: http://arxiv.org/abs/2510.14740v2
• Date: Fri, 31 Oct 2025 18:15:04 GMT
• Title: On Krylov Complexity as a Probe of the Quantum Mpemba Effect
• Authors: Mohsen Alishahiha, Mohammad Javad Vasli,
• Abstract summary: We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains.<n>For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings.<n>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 QME.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 QME, capturing anomalous relaxation even in cases where the total complexity fails to do so.

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