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

Valli, Angelo and Moca, Pascu Catalin and Werner, Miklós Antal and Kormos, Márton and Krajnik, Ziga and Prosen, Tomaz and Zaránd, Gergely Attila (2025) Efficient Computation of Cumulant Evolution and Full Counting Statistics: Application to Infinite Temperature Quantum Spin Chains. PHYSICAL REVIEW LETTERS, 135. No.-100401. ISSN 0031-9007

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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.

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