# Non-equilibrium dynamic critical scaling of the transverse-field Ising chain

**Speaker:**Michael Kolodrubetz, Princeton University

**When:**February 16, 2012 (Thu), 01:00PM to 02:00PM (add to my calendar)

**Location:**SCI 328

**Hosted by:**Anatoli Polkovnikov

*This event is part of the Condensed Matter Theory Seminar Series. *

Abstract:
The one-dimensional transverse-field Ising chain is a prototypical example of system that undergoes a continuous quantum phase transition. While its equilibrium scaling has been understood for more than half a century, I will discuss the non-equilibrium 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 talk, I will describe our solution for the full finite-size scaling functions of excess heat and spin-spin correlation function at an arbitrary time during the ramp. These scaling functions yield a number of surprises, including negative spin correlations on the ferromagnetic side of the transition, demonstrating qualitatively the athermal nature of the ramp. We then confirm the universality of the scaling functions by numerically simulating Mott-insulating bosons in a tilted potential, an experimentally-realizable system in the same universality class [J. Simon et. al., Nature **472**, 307 (2011)]. Our results indicate that the time scales necessary to see this dynamic scaling should be within the reach of present-day cold atom experiments.