Defect production in non-linear quench across a quantum critical point

Abstract

We show that the defect density $n$, for a slow non-linear power-law quench with a rate $\ddot{I}{„}^{-1}$ and an exponent $\hat{I}\pm >0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $\hat{I}½$ and $z$, scales as $n\sim \ddot{I}{„}^{-\hat{I}\pm \hat{I}½d/(\hat{I}\pm z\hat{I}½+1)}$ [$n\sim (\hat{I}\pm g^{(\hat{I}\pm -1)/\hat{I}\pm }/\ddot{I}„{)}^{\hat{I}½d/(z\hat{I}½+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0\ne 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($\hat{I}\pm =1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.

Final version; Accepted for publication in Physical Review Letters