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

Abstract

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 $\ensuremath{\tau}$ and exponent $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$. We discuss several experimental systems where these theoretical predictions can be tested.