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  • Letter
  • Open Access

Krylov complexity and confinement

Xuhao Jiang1,2, Jad C. Halimeh1,3,4,5, and N. S. Srivatsa3,4,*

  • *Contact author: srivatsa.nagara@mpq.mpg.de
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Phys. Rev. D 113, L031503 – Published 18 February, 2026

DOI: https://doi.org/10.1103/1gsg-zb8h

Abstract

In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed matter systems, for instance, in the Ising model with both transverse and longitudinal fields, where domain walls become confined into meson-like bound states as a result of a longitudinal field-induced linear potential. In this work, we employ the Ising model to demonstrate that Krylov state complexity—a measure quantifying the spread of quantum information under the repeated action of the Hamiltonian on a quantum state—serves as a sensitive and quantitative probe of confinement. We show that confinement manifests as a pronounced suppression of Krylov complexity growth following quenches within the ferromagnetic phase in the presence of a longitudinal field, reflecting slow correlation dynamics. In contrast, while quenches within the paramagnetic phase exhibit enhanced complexity with increasing longitudinal field, reflecting the absence of confinement, those crossing the critical point to the ferromagnetic phase reveal a distinct regime characterized by orders-of-magnitude larger complexity and display trends of weak confinement. Notably, in the confining regime, the complexity oscillates at frequencies corresponding to the meson masses, with its power-spectrum peaks closely matching the semiclassical predictions.

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Phys. Rev. D 113, L031503– Published 18 February, 2026
  • Received 14 November 2025
  • Accepted 28 January 2026
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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. Open access publication funded by the Max Planck Society.

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