Quench dynamics and defect production in the Kitaev and extended Kitaev models

TL;DR

This paper investigates quench dynamics and defect production in the Kitaev and extended Kitaev models, deriving scaling laws, exact correlation functions, and analyzing the effects of quench rate and model parameters.

Contribution

It provides new analytical results on defect scaling, correlation functions, and entropy in both 1D and 2D Kitaev models, including an extension to the 2D extended Kitaev model.

Findings

Defect density scales as 1/√τ in 1D Kitaev model.

Unconventional defect scaling across critical lines in 2D.

Derived general scaling law for defect density in d dimensions.

Abstract

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n \sim 1/\sqrt{\tau} where 1/\tau is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent non-zero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d dimensional quantum model, where the quench takes the system through a d-m dimensional gapless (critical) surface characterized by correlation length exponent \nu and dynamical critical exponent z, the defect density n \sim 1/\tau^{m \nu /(z \nu +1)}. We also discuss the variation of the shape and the spatial extent of the defect correlation function with the change of both the rate of quench and the model parameters and compute the entropy generated during such a quench process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.