Coherence-induced deep thermalization transition in random permutation quantum dynamics

TL;DR

This paper uncovers a phase transition in random permutation quantum dynamics where the system's post-measurement wavefunctions shift from a deep thermalized, maximally entropic state to a classical, minimally entropic state, revealing a new form of ergodicity-breaking.

Contribution

It introduces the concept of a deep thermalization transition in permutation dynamics, highlighting a novel ergodicity-breaking phenomenon not detectable through traditional thermalization measures.

Findings

Deep thermalization transition separates maximally entropic and classical ensembles.

Transition is controlled by coherence in the input state and measurement basis.

The transition is robust across different microscopic models.

Abstract

We report a phase transition in the projected ensemble - the collection of post-measurement wavefunctions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a type of quantum time evolution wherein computational basis states are shuffled without creating superpositions. It separates a phase exhibiting deep thermalization, where the projected ensemble is distributed over Hilbert space in a maximally entropic fashion (Haar-random), from a phase where it is minimally entropic ("classical bit-string ensemble"). Crucially, this deep thermalization transition is invisible to the subsystem's density matrix, which always exhibits thermalization to infinite-temperature across the phase diagram. Through a combination of analytical arguments and numerical simulations, we show that the transition is tuned by the total amount of coherence injected by the input state and the measurement basis, and is exhibited robustly across different microscopic models. Our findings represent a novel form of ergodicity-breaking universality in quantum many-body dynamics, characterized not by a failure of regular thermalization, but rather by a failure of deep thermalization.