# Thermalization and chaos in QED$_{3}$

## TL;DR

This paper investigates the thermalization process and quantum chaos in a 2+1 dimensional QED with many fermion flavors, revealing exponential growth in fermionic anti-commutators and calculating the Lyapunov exponent.

## Contribution

It provides the first leading-order calculation of fermionic anti-commutator growth and quantum Lyapunov exponent in this gauge theory, linking chaos to conformal field theory behavior.

## Key findings

- Anti-commutators grow exponentially, indicating chaos.
- Calculated quantum Lyapunov exponent for the theory.
- Discussed implications for locality and gauge invariance.

## Abstract

We study the real time dynamics of $N_F$ flavors of fermions coupled to a $U(1)$ gauge field in $2+1$ dimensions to leading order in a $1/N_F$ expansion. For large enough $N_{F}$, this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in $1/N_F$. We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.