Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems

Understand

The Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics.

• Only recently has the attention been paid to so-called full ETH, which accounts for higher-order correlations among matrix elements, and that can be rationalized theoretically using the language of Free Probability.
• In this work, we perform the first numerical investigation of the full ETH in physical many-body systems with local interactions by testing the decomposition of higher-order correlators into thermal free cumulants for local operators.
• We perform exact diagonalization on two classes of local non-integrable (chaotic) quantum many-body systems: spin chain Hamiltonians and Floquet brickwork unitary circuits.