24 research outputs found
Three dimensional resonating valence bond liquids and their excitations
We show that there are two types of RVB liquid phases present in
three-dimensional quantum dimer models, corresponding to the deconfining phases
of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite
cubic lattice and is the generalization of the critical point in the square
lattice quantum dimer model found originally by Rokhsar and Kivelson. The
latter exists on the non-bipartite face-centred cubic lattice and generalizes
the RVB phase found earlier by us on the triangular lattice. We discuss the
excitation spectrum and the nature of the ordering in both cases. Both phases
exhibit gapped spinons. In the U(1) case we find a collective, linearly
dispersing, transverse excitation, which is the photon of the low energy
Maxwell Lagrangian and we identify the ordering as quantum order in Wen's
sense. In the Z_2 case all collective excitations are gapped and, as in d=2,
the low energy description of this topologically ordered state is the purely
topological BF action. As a byproduct of this analysis, we unearth a further
gapless excitation, the pi0n, in the square lattice quantum dimer model at its
critical point.Comment: 9 pages, 2 figure
The Strong Energy Condition and the S-Brane Singularity Problem
Recently it has been argued that, because tachyonic matter satisfies the
Strong Energy Condition [SEC], there is little hope of avoiding the
singularities which plague S-Brane spacetimes. Meanwhile, however, Townsend and
Wohlfarth have suggested an ingenious way of circumventing the SEC in such
situations, and other suggestions for actually violating it in the S-Brane
context have recently been proposed. Of course, the natural context for
discussions of [effective or actual] violations of the SEC is the theory of
asymptotically deSitter spacetimes, which tend to be less singular than
ordinary FRW spacetimes. However, while violating or circumventing the SEC is
necessary if singularities are to be avoided, it is not at all clear that it is
sufficient. That is, we can ask: would an asymptotically deSitter S-brane
spacetime be non-singular? We show that this is difficult to achieve; this
result is in the spirit of the recently proved "S-brane singularity theorem".
Essentially our results suggest that circumventing or violating the SEC may not
suffice to solve the S-Brane singularity problem, though we do propose two ways
of avoiding this conclusion.Comment: 13 pages, minor corrections and improvements, references adde