Solvable model of deep thermalization with distinct design times

Matteo Ippoliti1 and Wen Wei Ho1,2

1Department of Physics, Stanford University, Stanford, CA 94305, USA
2Department of Physics, National University of Singapore, Singapore 117542

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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 $\textit{deep thermalization}$, 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.

A projective measurement on a part of a quantum system yields a random state in the rest of the system—but how random? Recent works suggest the emergence of a universal, maximally-random distribution of states at late times in generic quantum dynamics, a condition strictly stronger than conventional thermalization and potentially useful for quantum information processing tasks. Here we introduce a simple model of quantum dynamics where the emergence of this random distribution can be studied analytically thanks to random matrix methods.

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Cited by

[1] Pieter W. Claeys, "Universality in quantum snapshots", Quantum Views 7, 71 (2023).

[2] Minh C. Tran, Daniel K. Mark, Wen Wei Ho, and Soonwon Choi, "Measuring Arbitrary Physical Properties in Analog Quantum Simulation", arXiv:2212.02517, (2022).

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