Solvable model of deep thermalization with distinct design times

TL;DR

This paper introduces an exactly-solvable model demonstrating that deep thermalization, a strong form of quantum state equilibration, can occur at different timescales than regular thermalization, highlighting the roles of locality and imperfect thermalization.

Contribution

The paper presents a novel solvable model showing distinct timescales for deep thermalization and regular thermalization in quantum systems.

Findings

Deep thermalization occurs at a different time scale than regular thermalization.

The model confirms the role of locality and imperfect thermalization in universal wavefunction distributions.

Numerical simulations agree with analytical predictions.

Abstract

We study the emergence over time of a universal, uniform distribution of quantum states supported on a finite subsystem, induced by projectively measuring the rest of the system. Dubbed deep thermalization, this phenomenon represents a form of equilibration in quantum many-body systems stronger than regular thermalization, which only constrains the ensemble-averaged values of observables. While there exist quantum circuit models of dynamics in one dimension where this phenomenon can be shown to arise exactly, these are special in that deep thermalization occurs at precisely the same time as regular thermalization. Here, we present an exactly-solvable model of chaotic dynamics where the two processes can be shown to occur over different time scales. The model is composed of a finite subsystem coupled to an infinite random-matrix bath through a small constriction, and highlights the role of locality and imperfect thermalization in constraining the formation of such universal wavefunction distributions. We test our analytical predictions against exact numerical simulations, finding excellent agreement.