Work

Free Cumulants in Full Eigenstate Thermalization from Boundary Scrambling

Year: 2026

Type: article

Abstract: Out-of-time-order correlation functions (OTOCs) and their higher-order generalizations present important probes of quantum information dynamics and scrambling. We introduce a solvable many-body quantum model, which we term , for which the full dynamics of higher-order OTOCs is analytically tractable. Following recent extensions of the eigenstate thermalization hypothesis, these dynamics are encoded in free cumulants describing higher-order correlations between matrix elements. Using this correspondence, we obtain analytical predictions for time- and frequency-resolved free cumulants and show these to be stable away from the solvable point. The solvability is enabled by the identification of a higher-order Markovian influence matrix, capturing the effect of the full system on a local subsystem. These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly solvable many-body models.

Source: PRX Quantum

DOI: 10.1103/6n9v-b3b7

Authors: Felix Fritzsch, Gabriel O. Alves, Michael A. Rampp, Pieter W. Claeys

Institutions: Max Planck Institute for the Physics of Complex Systems, Trinity College Dublin

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

Funders: European Commission, Max-Planck-Gesellschaft, HORIZON EUROPE Framework Programme