1112.6422 (Michael Kolodrubetz et al.)

Nonequilibrium dynamic critical scaling of the quantum Ising chain    [PDF]

Michael Kolodrubetz, Bryan K. Clark, David A. Huse

The one-dimensional transverse-field Ising chain is a prototypical example of
a quantum phase transition. While its equilibrium scaling has been understood
for more than half a century, here we investigate the nonequilibrium quantum
critical dynamics as the system is swept slowly through the critical point (a
Kibble-Zurek ramp). Kibble-Zurek scaling is well understood for ramps that end
at the quantum critical point or deep in the ordered phase. In this Letter, we
solve for the full finite-size scaling forms of excess heat and spin-spin
correlation function for an arbitrary time during the ramp. On the
ferromagnetic side of the transition, we see negative spin correlations at a
distance set by the ramp rate, demonstrating qualitatively the athermal nature
of the ramp. We then confirm the universality of the scaling forms by
numerically simulating Mott-insulating bosons in a tilted potential, an
experimentally-realizable system in the same universality class. Our results
indicate that the time scales necessary to see this dynamic scaling should be
within the reach of present-day cold atom experiments.

View original: http://arxiv.org/abs/1112.6422