Probing thermality beyond the diagonal

TL;DR

This paper explores the off-diagonal elements of eigenstate thermalization in 2D conformal field theories using modular bootstrap and Virasoro blocks, confirming thermality signatures and entropic suppression.

Contribution

It introduces a novel analysis of OPE coefficient asymptotics and applies semi-classical Virasoro blocks to probe off-diagonal matrix elements in CFTs.

Findings

Off-diagonal elements show signatures of thermality.

Entropic suppression of off-diagonal elements is confirmed.

Modular bootstrap effectively extracts off-diagonal behavior.

Abstract

We investigate the off-diagonal sector of eigenstate thermalization using both local and non-local probes in 2-dimensional conformal field theories. A novel analysis of the asymptotics of OPE coefficients via the modular bootstrap is performed to extract the behaviour of the off-diagonal matrix elements. We also probe this sector using semi-classical heavy-light Virasoro blocks. The results demonstrate signatures of thermality and confirms the entropic suppression of the off-diagonal elements as necessitated by the eigenstate thermalization hypothesis.