Quantum quench, large N, and symmetry restoration

We globally quench the theory of two dimensional massless fermions (many flavours) with quartic interactions by making the quartic coupling a smooth function of time. Working in a derivative expansion we show that the discrete Z2 symmetry in case of the Gross-Neveu model, and the U(1) symmetry in case of the Nambu-Jona-Lasinio model, are restored during the zero-temperature quench. For the Gross-Neveu model we show that this can be understood as an effective thermalization. The time of symmetry restoration shows scaling with the quench rate. We identify this with the Kibble-Zurek scaling in the problem. In a suitable double scaling limit, the symmetry restoration may be understood in terms of Liouville quantum mechanics.