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

Abstract

We show that for a d-dimensional model in which a quench with a rate τ^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/τ^{mν/(zν+1)}, where νand 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=ν=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.

4 pages including 4 figures; generalized the discussion of the defect density scaling to the case of arbitrary critical exponents, and added some references; this version will appear in Physical Review Letters