  We present an exact solution for a quantum spin chain driven through its
critical points. Our approach is based on a many-body generalization of the
Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The
resulting nonequilibrium state of the system, while being a pure quantum state,
has local properties of a mixed state characterized by finite entropy density
associated with Kibble-Zurek defects. The entropy, as well as the finite spin
correlation length, are functions of the rate of sweep through the critical
point. We analyze the anisotropic XY spin 1/2 model evolved with a full
many-body evolution operator. With the help of Toeplitz determinants calculus,
we obtain an exact form of correlation functions. The properties of the evolved
system undergo an abrupt change at a certain critical sweep rate, signaling
formation of ordered domains. We link this phenomenon to the behavior of
complex singularities of the Toeplitz generating function.
