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 ${\tau }^{-1}$ and an exponent $\alpha >0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $\nu$ and $z$, scales as $n\sim {\tau }^{-\alpha \nu d/(\alpha z\nu +1)}$ [$n\sim (\alpha g^{(\alpha -1)/\alpha }/\tau {)}^{\nu d/(z\nu +1)}$], 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 ($\alpha =1$) 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

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