Probing thermality beyond the diagonal

Abstract

We investigate the off-diagonal sector of eigenstate thermalization using both local and nonlocal probes in two-dimensional conformal field theories. A novel analysis of the asymptotics of operator product expansion coefficients via the modular bootstrap is performed to extract the behavior of the off-diagonal matrix elements. We also probe this sector using semiclassical heavy-light Virasoro blocks. The results demonstrate signatures of thermality and confirm the entropic suppression of the off-diagonal elements as necessitated by the eigenstate thermalization hypothesis.