Universality of Quantum Information in Chaotic CFTs

TL;DR

This paper investigates the Eigenstate Thermalization Hypothesis in chaotic conformal field theories, demonstrating universality of reduced density matrices and their relation to black hole entropy in holographic systems.

Contribution

It provides a universal description of reduced density matrices in chaotic CFTs and connects ETH to holographic black hole entropy, extending to spatially varying coherent states.

Findings

ETH density matrix is universal in 2D CFTs with same central charge.

Reduced density matrix approximates the microcanonical ensemble.

Entropy comparison supports ETH in holographic systems.

Abstract

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.