Defect production due to quenching through a multicritical point

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as $t/\tau$, where $\tau$ is the characteristic time scale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects ($n$) in the final state is not necessarily given by the Kibble-Zurek scaling form $n \sim 1/\tau^{d \nu/(z \nu +1)}$, where $d$ is the spatial dimension, and $\nu$ and $z$ are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by $n \sim 1/\tau^{d/(2z_2)}$, where the exponent $z_2$ determines the behavior of the off-diagonal term of the $2 \times 2$ Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.