Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder

Understand

We study the non-equilibrium slow dynamics for the Kitaev model both in the presence and the absence of disorder.

• For the case without disorder, we demonstrate, via an exact solution, that the model provides an example of a system with an anisotropic critical point and exhibits unusual scaling of defect density $n$ and residual energy $Q$ for a slow linear quench.
• We provide a general expression for the scaling of $n$ ($Q$) generated during a slow power-law dynamics, characterized by a rate $\tau^{-1}$ and exponent $\alpha$, from a gapped phase to an anisotropic quantum critical point in $d$ dimensions, for which the energy gap $\Delta_{\vec k} \sim k_i^z$ for $m$ momentum components ($i=1..m$) and $\sim k_i^{z'}$ for the rest $d-m$ components ($i=m+1..d$) with $z\le z'$: $n \sim \tau^{-[m + (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$ ($Q \sim \tau^{-[(m+z)+ (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$).
• These general expressions reproduce both the corresponding results for the Kitaev model as a special case for $d=z'=2$ and $m=z=\nu=1$ and the well-known scaling laws of $n$ and $Q$ for isotropic critical points for $z=z'$.