Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains

TL;DR

This paper introduces a numerical method for efficiently computing quantum generating functions in 1D quantum systems at high temperature, enabling high-accuracy cumulant estimates and full counting statistics, with applications to spin chains.

Contribution

The authors develop a novel numerical approach that extends the accessible time scales for quantum spin chain simulations, challenging existing universality conjectures.

Findings

Reaches unprecedented time scales in spin chain simulations.

Challenges the Kardar-Parisi-Zhang universality conjecture.

Provides high-accuracy cumulant and full counting statistics estimates.

Abstract

We propose a numerical method to efficiently compute quantum generating functions (QGF) 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 QGF. We demonstrate its potential on spin $S=1/2$ anisotropic Heisenberg chain, where we can reach time scales 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.