Thermalization of Yang-Mills theory in a $(3+1)$ dimensional small lattice system

TL;DR

This paper investigates the real-time thermalization process of SU(2) Yang-Mills theory on a small 3+1D lattice after a quench, revealing temperature-dependent relaxation times and analyzing wave function dynamics.

Contribution

It provides a numerical study of thermalization in a small lattice Yang-Mills system, solving the Schrödinger equation with Gauss law constraints and analyzing relaxation times and wave function behavior.

Findings

Wilson loop thermalizes to the canonical state with a universal relaxation time.

Relaxation time is approximately 2π divided by the steady-state temperature.

Loschmidt echo analysis offers insights into the relaxation dynamics.

Abstract

We study the real-time evolution of SU($2$) Yang-Mills theory in a $(3+1)$ dimensional small lattice system after interaction quench. We numerically solve the Schr{\"o}dinger equation with the Kogut-Susskind Hamiltonian in the physical Hilbert space obtained by solving Gauss law constraints. We observe the thermalization of a Wilson loop to the canonical state; the relaxation time is insensitive to the coupling strength, and estimated as $\tau_{\rm eq}\sim 2\pi/T$ with temperatures $T$ at steady states. We also compute the vacuum persistence probability (the Loschmidt echo) to understand the relaxation from the dynamics of the wave function.