Showing papers by "Shivaji Lal Sondhi published in 2005"
TL;DR: It is shown that 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.
Abstract: The low-temperature entropy of the spin ice compounds, such as ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Dy}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, 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 $T=0$ 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.
165 citations
TL;DR: In this article, a family of rotationally invariant, local, $S=1∕2$ Klein Hamiltonians on various lattices that exhibit ground-state manifolds spanned by nearest-neighbor valence bond states was constructed.
Abstract: We construct a family of rotationally invariant, local, $S=1∕2$ Klein Hamiltonians on various lattices that exhibit ground-state manifolds spanned by nearest-neighbor valence bond states. We show that with selected perturbations such models can be driven into phases modeled by well-understood quantum dimer models on the corresponding lattices. Specifically, we show that the perturbation procedure is arbitrarily well controlled by a new parameter which is the extent of decoration of the reference lattice. This strategy leads to Hamiltonians that exhibit (i) ${Z}_{2}$ resonating valence bond (RVB) phases in two dimensions, (ii) $U(1)$ RVB phases with a gapless ``photon'' in three dimensions, and (iii) a Cantor deconfined region in two dimensions. We also construct two models on the pyrochlore lattice, one model exhibiting a ${Z}_{2}$ RVB phase and the other a $U(1)$ RVB phase.
51 citations
TL;DR: It is argued 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.
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.
48 citations
Journal Article•
1 citations