Regular Article

Order parameter dynamics of the non-linear sigma model in the large N limit

¹ Fakultät Physik, Technische Universität Dresden, 01069 Dresden, Germany
² Laboratory of Atomic And Solid State Physics, Cornell University, Ithaca, NY 14853, USA
³ Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway
⁴ School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
⁵ Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada

^a e-mail: ipsita.mandal@gmail.com

Received: 13 September 2019
Received in final form: 17 December 2019
Published online: 4 March 2020

Abstract

We study non-equilibrium order parameter dynamics of the non-linear sigma model in the large N limit, using Keldysh formalism. We provide a scheme for obtaining stable numerical solution of the Keldysh saddle point equations and use them to study order parameter dynamics of the model either following a ramp, or in the presence of a periodic drive. We find that the transient dynamics of the order parameter in the presence of a periodic drive is controlled by the drive frequency displaying the phenomenon of synchronization. We also study the approach of the order parameter to its steady state value following a ramp and find out the effective temperature of the steady state. We chart out the steady state temperature of the ordered phase as a function of ramp time and amplitude, and discuss the relation of our results to experimentally realizable spin models.