General Eigenstate Thermalization via Free Cumulants in Quantum Lattice
Systems
- URL: http://arxiv.org/abs/2303.00713v3
- Date: Mon, 31 Jul 2023 09:04:34 GMT
- Title: General Eigenstate Thermalization via Free Cumulants in Quantum Lattice
Systems
- Authors: Silvia Pappalardi, Felix Fritzsch and Toma\v{z} Prosen
- Abstract summary: We show that the dynamics of four-time correlation functions are encoded in fourth-order free cumulants.
Their non-trivial frequency dependence encodes the physical properties of local many-body systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 general 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 general ETH in physical many-body
systems with local interactions by testing the decomposition of higher-order
correlators into free cumulants. We perform exact diagonalization on two
classes of local non-integrable (chaotic) quantum many-body systems: spin chain
Hamiltonians and Floquet brickwork unitary circuits. We show that the dynamics
of four-time correlation functions are encoded in fourth-order free cumulants,
as predicted by ETH. Their non-trivial frequency dependence encodes the
physical properties of local many-body systems and distinguishes them from
structureless, rotationally invariant ensembles of random matrices.
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