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Efficient Computation of Cumulant Evolution and Full Counting Statistics: Application to Infinite Temperature Quantum Spin Chains

Angelo Valli1,2,3, Cătălin Paşcu Moca4,2, Miklós Antal Werner1,5, Márton Kormos1,2,3, Žiga Krajnik6, Tomaž Prosen7,8, and Gergely Zaránd1,2

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Phys. Rev. Lett. 135, 100401 – Published 3 September, 2025

DOI: https://doi.org/10.1103/f3c4-n21z

Abstract

We propose a numerical method to efficiently compute quantum generating functions for a wide class of observables in one-dimensional quantum systems at high temperature. We obtain high-accuracy estimates for the cumulants and reconstruct full counting statistics from the quantum generating functions. We demonstrate its potential on spin S=1/2 anisotropic Heisenberg chain, where we can reach timescales hitherto inaccessible to state-of-the-art classical and quantum simulations. Our results challenge the conjecture of the Kardar-Parisi-Zhang universality for isotropic integrable quantum spin chains.

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Phys. Rev. Lett. 135, 100401– Published 3 September, 2025
  • Received 10 November 2024
  • Revised 30 June 2025
  • Accepted 22 July 2025
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