Defect production due to quenching through a multicritical point

Abstract

We study the generation of defects when a quantum spin system is quenchedthrough a multicritical point by changing a parameter of the Hamiltonian ast/τ,where τ is the characteristic timescale of quenching. We argue that when a quantumsystem is quenched across a multicritical point, the density of defects(n) in the final state is not necessarily given by the Kibble–Zurek scaling formn∼1/τdν/(zν+1), whered is the spatialdimension, and ν and z are respectively the correlation length and dynamical exponent associated with the quantumcritical point. We propose a generalized scaling form of the defect density given byn∼1/τd/(2z2), where theexponent z2 determines the behavior of the off-diagonal term of the2 × 2 Landau–Zener matrix at the multicritical point. This scaling is valid not only at amulticritical point but also at an ordinary critical point.