Defect production in nonlinear quench across a quantum critical point

Abstract

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.