Kink-kink correlations in nonlinear quenches across a quantum critical point

TL;DR

This paper investigates the universal properties of kink-kink correlations in the 1D transverse field Ising model during nonlinear quenches across a quantum critical point, revealing dependence on multiple length scales and non-exponential decay of correlations.

Contribution

It extends the understanding of quench dynamics by analyzing how nonlinear quench protocols affect correlation functions and identifying the roles of different length scales.

Findings

Correlator depends only on KZ length for superlinear quenches.

An additional dephasing length is needed for other quench types.

Dephased correlator decays as a compressed exponential with a continuous exponent.

Abstract

When a quantum system exhibiting a second order phase transition is quenched across the critical point in large but finite time, the dynamics are not adiabatic in the critical region and the Kibble-Zurek (KZ) mechanism provides a framework to determine local observables such as the mean defect density. However, to find higher-point functions, one has to go beyond the KZ paradigm asshown in recent works on one-dimensional transverse field Ising model (TFIM) following a linear quench. It has been found that (i) besides the KZ scale, the quench dynamics depend on another length scale that arises due to the finite phase difference between the low energy modes, and (ii) contrary to the expectations based on the KZ mechanism, in general, the correlation functions do not decay exponentially with distance. Motivated by these results for the linear quench, we are interested in understanding if these properties are universal, and consider the 1D TFIM when the transverse field varies algebraically in the vicinity of the critical field. We focus on the equal-time,longitudinal kink-kink correlation function at the end of the quench from the paramagnetic to the ferromagnetic phase, and find that (i) the correlator depends only on the KZ length for superlinear quenches, otherwise an additional dephasing length is required to describe it, and (ii) the dephased correlator decays as a compressed exponential with an exponent that changes continuously with the quench exponent. Our results are obtained using an adiabatic perturbation theory, analytical arguments and exact numerical integration of the relevant equations.