# Quantum thermalization and Virasoro symmetry

## TL;DR

This paper investigates high energy matrix elements in 2d conformal field theories to assess the eigenstate thermalization hypothesis, revealing universal patterns consistent with thermalization in such theories.

## Contribution

It introduces an efficient oscillator-based method to compute matrix elements of primary operators in high energy Virasoro descendant states in 2d CFTs.

## Key findings

- Diagonal matrix elements vary smoothly with energy.
- Off-diagonal elements are power-law suppressed.
- Results support compatibility of 2d CFTs with ETH.

## Abstract

We initiate a systematic study of high energy matrix elements of local operators in 2d CFT. Knowledge of these is required in order to determine whether the eigenstate thermalization hypothesis (ETH) can hold in such theories. Most high energy states are high level Virasoro descendants, and by employing an oscillator representation of the Virasoro algebra we develop an efficient method for computing matrix elements of primary operators in such states. In parameter regimes where we expect (e.g. from AdS/CFT intuition) thermalization to occur, we observe striking patterns in the matrix elements: diagonal matrix elements are smoothly varying and off-diagonal elements, while nonzero, are power-law suppressed compared to the diagonal elements. We discuss the implications of these universal properties of 2d CFTs in regard to their compatibility with ETH.