Exact results for quench dynamics and defect production in a two-dimensional model

TL;DR

This paper derives an exact scaling law for defect production during quenches across critical surfaces in d-dimensional models, exemplified by the 2D Kitaev model, and provides correlation function calculations for defect analysis.

Contribution

It introduces a general scaling law for defect density in quenched systems crossing critical surfaces and offers the first exact multispin correlation function calculations in a 2D model.

Findings

Defect density scales as 1/τ^{mν/(zν+1)} across critical surfaces.

Kitaev model exemplifies the scaling with d=2, m=ν=z=1.

Exact multispin correlation functions are computed for the 2D model.

Abstract

We show that for a d-dimensional model in which a quench with a rate \tau^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/\tau^{m\nu/(z\nu +1)}, where \nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m=\nu=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.