Eigenstate Thermalization in Long-Range Interacting Systems

TL;DR

This paper investigates the eigenstate thermalization hypothesis in long-range quantum systems with power-law interactions, finding it generally holds for certain interaction strengths but breaks down for others, especially at lower exponents.

Contribution

It provides numerical evidence for the validity and limitations of the strong ETH in long-range interacting systems with power-law decay.

Findings

Strong ETH holds for $oldsymbol{ ext{}\alpha extgreater 0.6}$.

Eigenstate expectation values deviate from microcanonical averages in long-range systems.

Srednicki's ansatz breaks down for $oldsymbol{ ext{ extless} 1.0}$ at large system sizes.

Abstract

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.