A simple theory for quantum quenches in the ANNNI model

TL;DR

This paper develops a simple mean-field theory to accurately describe quantum quenches in the ANNNI model, explaining observed critical point signatures and oscillatory behaviors in post-quench dynamics.

Contribution

It introduces a time-dependent mean-field approach that captures short-time quench dynamics in the ANNNI model with high accuracy, elucidating the origin of oscillations and limitations in detecting quantum critical points.

Findings

Mean-field theory accurately describes early-time quench dynamics.

Oscillations originate from long-lived bound states.

Limits on detecting quantum critical points via quenches are identified.

Abstract

In a recent numerical study by Haldar et al. (Phys. Rev. X 11, 031062) it was shown that signatures of proximate quantum critical points can be observed at early and intermediate times after certain quantum quenches. Said work focused mainly on the case of the axial next-nearest neighbour Ising (ANNNI) model. Here we construct a simple time-dependent mean-field theory that allows us to obtain a quantitatively accurate description of these quenches at short times, which for reasons we explain remains a fair approximation at late times (with some caveats). Our approach provides a simple framework for understanding the reported numerical results as well as fundamental limitations on detecting quantum critical points through quench dynamics. We moreover explain the origin of the peculiar oscillatory behaviour seen in various observables as arising from the formation of a long-lived bound state.