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 $τ^{-1}$ and an exponent $α>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ν$ and $z$, scales as $n \sim τ^{-ανd/ (αzν+1)}$ [$n \sim (αg^{(α-1)/α}/τ)^{νd/(zν+1)}$], 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 ($α=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.