Shivaji Sondhi

Abstract:

Scaling arguments imply that quantum-critical points exhibit universal nonlinear responses to external probes. We investigate the origins of such nonlinearities in transport, which is especially problematic since the system is necessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism--the production of carriers from the vacuum by the applied field--which is then balanced against a scattering rate that is itself set by the field. We show by explicit computation how this works for the case of the symmetric superfluid-Mott insulator transition of bosons.

Abstract:

The low-temperature entropy of the spin ice compounds, such as and , is well described by the nearest-neighbor antiferromagnetic Ising model on the pyrochlore lattice, i.e., by the "ice rules." This is surprising since the dominant coupling between the spins is their long ranged dipole interaction. We show that this phenomenon can be understood rather elegantly: one can construct a model dipole interaction, by adding terms of shorter range, which yields precisely the same ground states, and hence entropy, as the nearest-neighbor interaction. A treatment of the small difference between the model and true dipole interactions reproduces the numerical work by Gingras et al. in detail. We are also led to a more general concept of projective equivalence between interactions.