Theory of defect production in nonlinear quench across a quantum critical point

We study defect production in a quantum system subjected to a nonlinear power-law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work [D. Sen, K. Sengupta, and S. Mondal, Phys. Rev. Lett. 101, 016806 (2008)] and present a detailed analysis of the scaling of the defect density n with the quench rate tau and exponent alpha for each of the above-mentioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent alpha. We discuss several experimental systems where these theoretical predictions can be tested