Quantum quench, large N, and symmetry restoration

Abstract

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 Z 2 symmetry in case of the Gross-Neveu model, and the U(1) symmetry in case of the Nambu-Jona-Lasinio 2 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.

Scrambling under quench

“…At finite temperatures both in the O(N ) non-linear sigma model [29] as well as the Gross-Neveu model [30] the Lyapunov exponent scales linearly with temperature at large N . Furthermore, the Schwinger-Keldysh formalism for studying quantum quenches have already been explored in these models [31,32].…”

Scrambling under quench

“…At finite temperatures both in the O(N ) non-linear sigma model [38] as well as the Gross-Neveu model [39] the Lyapunov exponent scales linearly with temperature at large N . Furthermore, the Schwinger-Keldysh formalism for studying quantum quenches have already been explored in these models [40,41]. It will be interesting to contrast the effective time-dependent temperature extracted from the Lyapunov index against that extracted from the time-dependent gap equation.…”