Continuum approach to real time dynamics of(1+1)Dgauge field theory: Out of horizon correlations of the Schwinger model

Ivan Kukuljan

doi:10.1103/physrevd.104.l021702

Abstract

We develop a truncated Hamiltonian method to study nonequilibrium real time dynamics in the Schwinger model - the quantum electrodynamics in D=1+1. This is a purely continuum method that captures reliably the invariance under local and global gauge transformations and does not require a discretisation of space-time. We use it to study a phenomenon that is expected not to be tractable using lattice methods: we show that the 1+1D quantum electrodynamics admits the dynamical horizon violation effect which was recently discovered in the case of the sine-Gordon model. Following a quench of the model, oscillatory long-range correlations develop, manifestly violating the horizon bound. We find that the oscillation frequencies of the out-of-horizon correlations correspond to twice the masses of the mesons of the model suggesting that the effect is mediated through correlated meson pairs. We also report on the cluster violation in the massive version of the model, previously known in the massless Schwinger model. The results presented here reveal a novel nonequilibrium phenomenon in 1+1D quantum electrodynamics and make a first step towards establishing that the horizon violation effect is present in gauge field theory.

Highlights

Computing real time dynamics of an interacting manybody quantum system is a notoriously difficult problem. It has been currently getting an overwhelming amount of attention due to the fast developing field of nonequilibrium physics both in high energy [1,2,3,4,5,6,7,8,9] and condensed matter physics [10,11,12] on one side and renewed interest in chaos and information scrambling on the other side [13,14,15,16,17]
The set of tools to deal with the problem has been greatly enriched by developments and new insights in integrability theory [22,23,24], holography [25,26,27,28,29] and numerical algorithms such as density matrix renormalization group (DMRG) [30,31], tensor networks (TNS) [32,33,34] and lattice gauge theory [35,36]
We focus here on the simplest example of a gauge field theory, the 1 þ 1D quantum electrodynamics (QED), i.e., the Schwinger model: L

Summary

Introduction

Computing real time dynamics of an interacting manybody quantum system is a notoriously difficult problem It has been currently getting an overwhelming amount of attention due to the fast developing field of nonequilibrium physics both in high energy [1,2,3,4,5,6,7,8,9] and condensed matter physics [10,11,12] on one side and renewed interest in chaos and information scrambling on the other side [13,14,15,16,17].

Methods

Results

Conclusion