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arXiv:2409.14442 · Physical Review Letters

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

Angelo Valli, Cătălin Paşcu Moca, Miklós Antal Werner, Márton Kormos, Žiga Krajnik, Tomaž Prosen, Gergely Zaránd

Published Jul 22, 2025• 10 citations
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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.

DOI
10.1103/f3c4-n21z

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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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Abstract Understanding universal behavior of far-from-equilibrium transport dynamics at a quantum many-body level is a longstanding challenge. A full characterization of universal dynamics of nonlocal correlation functions still remains largely unknown. In this letter, we uncover universal scaling laws of higher-order cumulants in one-dimensional isotropic Heisenberg model, revealing anomalous behaviors of nonequilibrium dynamics exclusively accessible in higher-order correlation functions. Using numerical simulations and full counting statistics, we determine the power laws of both the spin polarization transfer and contrast cumulants for different kinds of helix and domain-wall initial states. Building on such physical states, we unify the scaling behavior of the higher-order cumulants as two types of dynamics: anomalous diffusive and superdiffusive. For the former, these higher cumulants show a deviation from Gaussian statistics, with the scaling exponents being identical for the first four orders. For the latter, however, we observe a breakdown of KPZ universality, with the exponents of the third and fourth orders differing significantly from those of the first two. Our results are also agreeable with recent experimental observations, advancing understanding of far-from-equilibrium transport phenomena.
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