Semi-classical theory for quantum quenches in the O(3) non-linear sigma model

TL;DR

This paper develops a semi-classical framework to analyze non-equilibrium dynamics in the O(3) non-linear sigma model, predicting relaxation behaviors after quantum quenches and validating the approach against known models.

Contribution

It introduces a semi-classical method for studying quantum quenches in the O(3) non-linear sigma model, extending its applicability to related systems like the transverse field Ising chain.

Findings

Predicted quench-dependent relaxation times and correlation lengths.

Validated semi-classical results against exact and numerical solutions.

Identified the limits of the semi-classical approach.

Abstract

We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method.