  In this review, we study the quenching dynamics of a one-dimensional XY
Hamiltonian in a transverse field under linear variation of different
parameters of the Hamiltonian so that the system is driven through various
critical points and gapless lines. It is observed that the density of defects
falls off as a power law with the quenching rate $1/\tau$ where the power law
is determined by the dimensionality of the underlying lattice and the critical
exponents associated with the quantum critical point as predicted by
Kibble-Zurek scaling. However, we show that when the system is driven through a
multicritical point or along a gapless line, Kibble Zurek scaling needs to be
modified. We discuss generalized scaling forms of the defect density for the
above two situations.

Statistical Mechanics