Quantum quench in the attractive regime of the sine-Gordon model

TL;DR

This paper analytically investigates the late-time dynamics of the sine-Gordon model after a quantum quench into the attractive regime, revealing exponential decay and oscillatory behavior in the expectation value of a vertex operator, with implications for the power spectrum.

Contribution

The study provides an exact analytical framework for late-time dynamics of the sine-Gordon model post-quench, highlighting the role of breathers and form factors in the attractive regime.

Findings

Late-time expectation value decays exponentially with distinct rates.

Zero-momentum breathers cause oscillatory behavior in the dynamics.

Power spectrum exhibits smooth peaks near breather masses.

Abstract

We study the dynamics of the sine-Gordon model after a quantum quench into the attractive regime, where the spectrum consists of solitons, antisolitons and breathers. In particular, we analyse the time-dependent expectation value of the vertex operator, $\exp\left({\rm i}\beta\Phi/2\right)$, starting from an initial state in the "squeezed state form" corresponding to integrable boundary conditions. Using an expansion in terms of exact form factors, we compute analytically the leading contributions to this expectation value at late times. We show that form factors containing breathers only contribute to the late-time dynamics if the initial state exhibits zero-momentum breather states. The leading terms at late times exponentially decay, and we compute the different decay rates. In addition, the late-time contributions from the zero-momentum breathers display oscillatory behaviour, with the oscillation frequency given by the breather mass renormalised by interaction effects. Using our result, we compute the low-energy contributions to the power spectrum of the vertex operator. The oscillatory terms in the expectation value are shown to produce smooth peaks in the power spectrum located near the values of the bare breather masses.