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 that can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

• Received 12 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.077204