Eigenstate Thermalization in Long-Range Interacting Systems

Motivated by recent ion experiments on tunable long-range interacting quantum systems [B.Neyenhuis et al., Sci.Adv.3, e1700672 (2017, https://doi.org/10.1126/sciadv.1700672 )], we test the strong eigenstate thermalization hypothesis (ETH) for systems with power-law interactions $\sim 1/r^{\alpha}$. We numerically demonstrate that the strong ETH typically holds at least for systems with $\alpha\geq 0.6$, 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 $\alpha \lesssim 1.0$ at least for relatively large system sizes.