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Coherence-Induced Deep Thermalization Transition in Random Permutation Quantum Dynamics
Chang Liu1, Matteo Ippoliti2, Wen Wei Ho1,3
1National University of Singapore, Department of Physics, Singapore 117551.
Physical Review Letters
|March 27, 2026
Summary
Researchers discovered a phase transition in quantum systems undergoing random permutation dynamics. This transition separates deep thermalization from a classical state, even though subsystem measurements always appear thermal.
Area of Science:
- Quantum Mechanics
- Many-Body Physics
- Statistical Mechanics
Background:
- Quantum systems can exhibit thermalization, where they reach a state of maximum entropy.
- Deep thermalization describes a more specific state where subsystem properties are Haar random.
- Random permutation dynamics shuffle states without creating superpositions, offering a unique model for studying quantum evolution.
Purpose of the Study:
- To identify and characterize a phase transition in the projected ensemble of quantum systems.
- To investigate the conditions under which deep thermalization occurs and how it differs from standard thermalization.
- To explore the role of coherence and measurement basis in driving this transition.
Main Methods:
- Analysis of the projected ensemble, which consists of postmeasurement wave functions of a local subsystem.
- Studying systems undergoing random permutation dynamics.
- Employing analytical arguments and numerical simulations across various microscopic models.
Main Results:
- A phase transition was identified, separating a deep thermalization phase (maximally entropic projected ensemble) from a classical bit-string ensemble (minimally entropic).
- This deep thermalization transition is undetectable via the subsystem's density matrix, which consistently shows infinite-temperature thermalization.
- The transition is tunable by input state coherence and measurement basis, and is robust across different models.
Conclusions:
- A novel form of ergodicity-breaking universality exists in quantum many-body dynamics.
- This universality is characterized by a failure of deep thermalization, not a failure of standard thermalization.
- The projected ensemble provides a sensitive probe for detecting subtle quantum phenomena invisible to subsystem density matrices.
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