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Local ergotropy dynamically witnesses many-body localized phases

F. Formicola1,*,†, G. Di Bello1,*,‡, G. De Filippis2,3, V. Cataudella2,3, D. Farina1,3, and C. A. Perroni2,3

  • *These authors contributed equally to this work.
  • †Contact author: francesco.formicola@unina.it
  • ‡Contact author: grazia.dibello@unina.it
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Phys. Rev. Research 7, 043086 – Published 22 October, 2025

DOI: https://doi.org/10.1103/2z1g-rgr9

Abstract

Many-body localization is a dynamical phenomenon characteristic of strongly interacting and disordered many-body quantum systems that fail to achieve thermal equilibrium. From a quantum information perspective, one of the most relevant fingerprints of this phenomenon is the logarithmic growth of the entanglement entropy over time. We perform intensive numerical simulations, applied to a paradigmatic model system, showing that the local ergotropy, the maximum extractable work via local unitary operations on a small subsystem in the presence of Hamiltonian coupling, dynamically witnesses the change from ergodic to localized phases. Within the many-body localized phase, both the local ergotropy and its quantum fluctuations slowly vary over time with a characteristic logarithmic law analogous to the behavior of entanglement entropy. This showcases how directly leveraging local control, instead of local observables or entropies analyzed in previous works, provides a thermodynamic marker of localization phenomena based on the locally extractable work.

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Phys. Rev. Research 7, 043086– Published 22 October, 2025
  • Received 12 March 2025
  • Accepted 3 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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