Eigenstate Thermalization in Long-Range Interacting Systems.

Motivated by recent ion experiments on tunable long-range interacting quantum systems [Neyenhuis et al., Sci. Adv. 3, e1700672 (2017)SACDAF2375-254810.1126/sciadv.1700672], we test the strong eigenstate thermalization hypothesis for systems with power-law interactions ∼1/r^{α}. We numerically demonstrate that the strong eigenstate thermalization hypothesis typically holds, at least for systems with α≥0.6, which include Coulomb, monopole-dipole, and dipole-dipole interactions. Compared with short-range interacting systems, the eigenstate expectation value of a generic local observable is shown to deviate significantly from its microcanonical ensemble average for long-range interacting systems. We find that Srednicki's ansatz breaks down for α≲1.0, at least for relatively large system sizes.

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. The ergodicity of our random matrix ensembles breaks down because of locality.