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Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
Silvia Pappalardi1,2, Felix Fritzsch3,4, Tomaž Prosen3,5
1Laboratoire de Physique de l'École Normale Supérieure, ENS, CNRS, F-75005 Paris, France.
Physical Review Letters
|April 25, 2025
Summary
This study numerically investigates the full eigenstate thermalization hypothesis (ETH) in quantum many-body systems. It confirms that higher-order correlations in chaotic systems align with predictions from free probability theory.
Area of Science:
- Quantum statistical mechanics
- Many-body physics
- Quantum chaos
Background:
- The eigenstate thermalization hypothesis (ETH) provides a framework for quantum statistical mechanics.
- Full ETH extends this by considering higher-order correlations, theoretically linked to free probability.
- Previous work has focused on theoretical aspects, lacking numerical validation in physical systems.
Purpose of the Study:
- To perform the first numerical investigation of the full ETH in physical many-body systems.
- To test the decomposition of higher-order correlators into thermal free cumulants for local operators.
- To explore the role of free probability in understanding quantum thermalization.
Main Methods:
- Exact diagonalization of local nonintegrable quantum many-body systems.
- Analysis of spin chain Hamiltonians and Floquet brickwork unitary circuits.
- Testing the decomposition of four-time correlation functions into fourth-order free cumulants.
Main Results:
- The dynamics of four-time correlation functions are successfully encoded in fourth-order free cumulants.
- This confirms predictions of the full ETH in the studied systems.
- Frequency dependence of these correlators reveals physical properties of many-body systems.
Conclusions:
- The study provides the first numerical evidence for the full ETH in physical systems.
- Free probability offers a powerful tool to rationalize and predict quantum thermalization dynamics.
- The findings distinguish chaotic quantum systems from random matrix ensembles based on their correlation functions.
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