The Multi-trace Eigenstate Thermalization Hypothesis
Abstract
We introduce a multi-trace eigenstate thermalization hypothesis, an extension of ETH that governs connected correlations of operator matrix elements with arbitrary index structures, including several disjoint index cycles. We derive multi-trace ETH from local rotational invariance, relate its independent data to higher-order free cumulants, and construct a cyclic matrix model that encodes the resulting multi-cycle data. We provide evidence for multi-trace ETH in chaotic quantum systems and compute multi-trace correlations in low-dimensional gravity. In few-body systems, multi-trace contributions arise from correlated periodic orbits, including a linear ramp contribution to the one-point spectral form factor. In two dimensions, we compute interaction-induced multi-trace correlations from a quartically coupled bulk scalar in JT gravity, relating winding matter diagrams to corrections of matter-channel weights and anomalous dimensions. In three dimensions, we show that multi-trace non-Gaussianities arise from both topology-changing saddles and light matter. Using Virasoro TQFT and conformal mean-field theory, we compute examples involving knot and link complements and torus wormholes with matter loops. Across these settings, multi-trace ETH provides a common framework for both connected correlators in chaotic quantum systems and multi-boundary wormhole amplitudes in gravity.
Related
- A random sampling method to test the weak Eigenstate Thermalization Hypothesis
- Predicting dynamics from flows of the eigenstate thermalization hypothesis
- Full Eigenstate Thermalization in Quantum Field Theory and Gravitational Scrambling
- Full Eigenstate Thermalization in Quantum Field Theory: Free Cumulants and Gravitational Scrambling
- Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems
BibTeX
@misc{abdalla2026multitrace,
title = {{The Multi-trace Eigenstate Thermalization Hypothesis}},
author = {Ahmed I. Abdalla and Gabriele Di Ubaldo and Elisa Tabor},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00197},
eprint = {2611.00197},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00197},
}
RIS
TY - UNPB
TI - The Multi-trace Eigenstate Thermalization Hypothesis
AU - Ahmed I. Abdalla
AU - Gabriele Di Ubaldo
AU - Elisa Tabor
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00197
UR - https://arxiv.org/abs/2611.00197
AB - We introduce a multi-trace eigenstate thermalization hypothesis, an extension of ETH that governs connected correlations of operator matrix elements with arbitrary index structures, including several disjoint index cycles. We derive multi-trace ETH from local rotational invariance, relate its independent data to higher-order free cumulants, and construct a cyclic matrix model that encodes the resulting multi-cycle data. We provide evidence for multi-trace ETH in chaotic quantum systems and compute multi-trace correlations in low-dimensional gravity. In few-body systems, multi-trace contributions arise from correlated periodic orbits, including a linear ramp contribution to the one-point spectral form factor. In two dimensions, we compute interaction-induced multi-trace correlations from a quartically coupled bulk scalar in JT gravity, relating winding matter diagrams to corrections of matter-channel weights and anomalous dimensions. In three dimensions, we show that multi-trace non-Gaussianities arise from both topology-changing saddles and light matter. Using Virasoro TQFT and conformal mean-field theory, we compute examples involving knot and link complements and torus wormholes with matter loops. Across these settings, multi-trace ETH provides a common framework for both connected correlators in chaotic quantum systems and multi-boundary wormhole amplitudes in gravity.
ER -