Quenches as probes of quantum phase transitions

This numerical paper has some fascinating results, and the germ of a very clever idea (I heard about this work via Andy Millis):

Dynamical phase transition in correlated fermionic lattice systems
Martin Eckstein, Marcus Kollar, Philipp Werner
http://arxiv.org/abs/0904.0976

Abstract: We use non-equilibrium dynamical mean-field theory to demonstrate the existence of a critical interaction in the real-time dynamics of the Hubbard model after an interaction quench. The critical point is characterized by fast thermalization and separates weak-coupling and strong-coupling regimes in which the relaxation is delayed due to prethermalization on intermediate timescales. This dynamical phase transition should be observable in experiments on trapped fermionic atoms.

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So what they do is quench the interaction strength and see how long it takes the system to thermalize. In general when you quench into a gapped state, thermalization can take a really long time because particles trapped on the wrong side of the gap don't have anything to decay into. (See here.) On the other hand, e.g. near a quantum phase transition, the gap is small and thermalization should be easy. So by looking at how long a system takes to approach equilibrium as you quench from a reference parameter value to some value U_f, you can essentially map out a quantum phase diagram and maybe get some information about the exponents. [I should note that this is all somewhat speculative.] What's particularly interesting about the Kollar/Eckstein case is that they didn't even know there was a phase transition there until they did their simulations.

There's some recent work on (possibly) similar ideas that I haven't read yet:

Quench dynamics as a probe of quantum criticality
Authors: R. A. Barankov
http://arxiv.org/abs/0910.0255

Abstract: Quantum critical points of many-body systems can be characterized by studying response of the ground-state wave function to the change of the external parameter, encoded in the ground-state fidelity susceptibility. This quantity characterizes the quench dynamics induced by sudden change of the parameter. In this framework, I analyze scaling relations concerning the probability of excitation and the excitation energy, with the quench amplitude of this parameter. These results are illustrated in the case of one-dimensional sine-Gordon model.