FisMat2017 - Submission - View

Abstract's title: Macroscopic chaos induced by quantum fluctuations near a dynamical phase transition
Submitting author: Alessio Lerose
Affiliation: SISSA Trieste
Affiliation Address: Via Bonomea, 265 34136 - Trieste
Country: Italy
Oral presentation/Poster (Author's request): Poster
Other authors and affiliations: Jamir Marino Institut fu¨r Theoretische Physik, Universita¨t zu K¨oln, D-50937 Cologne, Germany Bojan Zunkovic Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia Andrea Gambassi SISSA — International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy INFN — Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34136 Trieste, Italy Alessandro Silva SISSA — International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy

In recent years, the dynamical consequences of spontaneous symmetry breaking have been investigated: What is the fate of the order parameter when the system is driven away from equilibrium?

Mean-field analyses suggest that dynamical criticality sistematically appears. However, they rigorously describe unrealistic infinite-range of infinite-dimensional limits, where few collective macroscopic variables play a role and all the microscopic degrees of freedom, associated with spatial fluctuations, are frozen. It is a matter of principle to understand whether such dynamical criticality is robust to the inclusion of fluctuations (that are present even at zero temperature in quantum systems): will they be able to drive the system to thermal equilibrium, and hence to trivialize the dynamical critical phenomenon into a standard equilibrium transition? If so, the above dynamical criticality would just represent a mean-field artefact.

We address this problem by studying the off-equilibrium dynamics of an infinite-range quantum Ising model in a transverse field with an additional short-range interaction. We present a viable systematic approach to deal with the time-evolution that goes beyond mean-field, in terms of a time-dependent spin-wave theory. The results are quite surprising: throughout the two phases the dynamical behavior of the order parameter remains largely unaffected by the coupling to the extensive "bath" of spatial fluctuations modes. On the other hand, such microscopic fluctuations turn out to have a deep impact on the dynamical critical point, giving rise to a whole new region with chaotic features, characterized by an "unpredictable" asymptotic dynamical order for long times. The latter non-trivial phenomenon, fully confirmed by numerical simulations of the full many-body quantum evolution, is completely absent at mean-field level.