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Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics

Doru Sticlet1, Balázs Dóra2,3, Dominik Szombathy2,4, Gergely Zaránd2,5, and Cătălin Paşcu Moca2,3,6,*

  • *Contact author: mocap@uoradea.ro
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Phys. Rev. Research 7, 043130 – Published 3 November, 2025

DOI: https://doi.org/10.1103/96bk-xf8p

Abstract

Magic, or nonstabilizerness, is a crucial quantum resource, yet its dynamics in open quantum systems remain largely unexplored. We investigate magic in the open XXZ spin chain under either boundary gain and loss or bulk dephasing using the stabilizer Rényi entropy M2. To enable scalable simulations of large systems, we develop a unique, highly efficient algorithm for computing M2 within the matrix product state formalism while maintaining constant bond dimension—an advancement over existing methods. For boundary driving, we uncover universal scaling laws, M2(t)∼t1/z, linked to the dynamical exponent z for several distinct universality classes. We also disentangle classical and quantum contributions to magic by introducing a mean-field approximation for magic, thus emphasizing the prominent role of quantum-critical fluctuations in nonstabilizerness. For bulk dephasing, dissipation can transiently enhance magic before suppressing it and drive it to a nontrivial steady-state value. These findings position magic as a powerful diagnostic tool for probing universality and dynamics in open quantum systems.

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Phys. Rev. Research 7, 043130– Published 3 November, 2025
  • Received 28 April 2025
  • Revised 19 June 2025
  • Accepted 26 September 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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