Defect Production in Nonlinear Quench across a Quantum Critical Point

We show that the defect density n, for a slow nonlinear 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~τ^-ανd/(αzν+1) [n~(αg^(α-1)/α/τ)^νd/(zν+1)] if the quench takes the system across the critical point at time $t=0$ [t=t₀≠0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a 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.