Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions

¹  Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory - Hanover, NH 03755, USA
²  Department of Physics, Indiana University - Bloomington, IN 47405, USA

Corresponding author: Lorenza.Viola@Dartmouth.EDU

Received: 23 July 2008
Accepted: 13 November 2008

Abstract

We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points (i.e., critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, we show how multiple level crossings within a gapless phase may completely suppress excitation depending on the control path. Our results typify non-ergodic scaling in continuous finite-order quantum phase transitions.