Restoration and Dynamical Breakdown of the \phi \to -\phi Symmetry in the (1+1)-dimensional Massive sine-Gordon Field Theory

TL;DR

This paper studies how quantum and finite-temperature effects influence the Z_2-symmetry in the (1+1)-dimensional massive sine-Gordon model, showing that quantum effects can both restore and break the symmetry, while temperature effects only restore it.

Contribution

It demonstrates the conditions under which quantum and thermal effects restore or break the Z_2-symmetry using the Gaussian wave-functional approach.

Findings

Quantum effects can restore Z_2-symmetry in some parameter regions.

Quantum effects can also cause spontaneous symmetry breaking.

Finite-temperature effects only lead to symmetry restoration.

Abstract

Within the framework of the Gaussian wave-functional approach, we investigate the influences of quantum and finite-temperature effects on the Z_2-symmetry(\phi \to -\phi) of the (1+1)-dimensional massive sine-Gordon field theory. It is explicitly demonstrated that by quantum effects the Z_2-symmetry can be restored in one region of the parameter space and dynamically spontaneously broken in another region. Moreover, a finite-temperature effect can further restore the Z_2-symmetry only.