Eigenstate Thermalization in Long-Range Interacting Systems.

Motivated by recent ion experiments on tunable long-range interacting quantum systems [Neyenhuis et al., Sci. Adv.

Test of the Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory.

We verify that the eigenstate thermalization hypothesis (ETH) holds universally for locally interacting quantum many-body systems. Introducing random matrix ensembles with interactions, we numerically obtain a distribution of maximum fluctuations of eigenstate expectation values for different realizations of interactions. This distribution, which cannot be obtained from the conventional random matrix theory involving nonlocal correlations, demonstrates that an overwhelming majority of pairs of local Hamiltonians and observables satisfy the ETH with exponentially small fluctuations.