Work

Free Probability in a Minimal Quantum Circuit Model

Year: 2026

Type: article

Abstract: Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multitime correlation functions. We consider the dynamics of higher-order out-of-time-order correlators (OTOCs) in a minimal circuit model for quantum dynamics. This model mimics the dynamics of a structured subsystem locally coupled to a maximally random environment. We prove the exponential decay of all higher-order OTOCs and fully characterize the relevant timescales, showing how local operators approach free independence at late times. We show that the effects of the environment on the local subsystem can be captured in a higher-order influence matrix, which allows for a Markovian description of the dynamics provided an auxiliary degree of freedom is introduced. This degree of freedom directly yields a dynamical picture for the OTOCs in terms of free cumulants from free probability, consistent with recent predictions from the full eigenstate thermalization hypothesis. This approach and the relevant influence matrix are expected to be applicable in more general settings and present a first step to characterizing quantum memory in higher-order OTOCs.

Source: Physical Review X

DOI: 10.1103/6mpz-p85s

Authors: Felix Fritzsch, 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: $4,200

Funders: European Commission, Max-Planck-Gesellschaft, HORIZON EUROPE Framework Programme, H2020 Marie Skłodowska-Curie Actions