Full eigenstate thermalization in integrable spin systems
Phys. Rev. E 114, 044124 – Published 15 October, 2026
DOI: https://doi.org/10.1103/n7yh-828k
Abstract
The Eigenstate Thermalization Hypothesis (ETH) is a standard tool to understand the thermalization properties of an isolated quantum system. Its generalization to higher-order correlations of matrix elements of local operators, dubbed the full ETH, relates the ETH free cumulants to the corresponding thermal free cumulants in the thermodynamic limit. In this work, we numerically test the full-ETH predictions using exact diagonalization of two integrable spin models: the Ising and the XXZ Heisenberg models. The differences from the behavior predicted by full ETH in chaotic systems are highlighted and contrasted along the way. We further study the out-of-time-ordered correlator (OTOC) through its approximate decomposition into contributions involving the second- and fourth-order ETH free cumulants. We find that, although the fourth-order contribution governs the late-time behavior of the OTOC in these integrable models, its dynamics differ significantly from that found in nonintegrable systems.
