We describe the nature of charge transport at non-zero temperatures (T ) above the two-dimensional (d) superfluid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order k B T /h. This implies that the transport at frequencies ω ≪ k B T /h is in the hydrodynamic, collision-dominated (or 'incoherent') regime, while ω ≫ k B T /h is the collisionless (or 'phasecoherent') regime. The conductivity is argued to be e 2 /h times a non-trivial universal scaling function ofhω/k B T , and not independent ofhω/k B T , as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamichω/k B T → 0 limit of this function, and is a universal number times e 2 /h, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionlesshω/k B T → ∞ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times e 2 /h. We provide the first computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in ǫ = 3 − d. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.

We discuss the theory of the nonzero temperature (T) spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap ⌬. For TӶ⌬, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle S matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the O(3) model, and strong-and weak-coupling expansions ͑the latter using a Majorana fermion represen-tation͒ for the two-leg Sϭ1/2 Heisenberg antiferromagnetic ladder. As an aside, we note that the strongcoupling calculation reveals an Sϭ1, two-particle bound state which leads to the presence of a second peak in the Tϭ0 inelastic neutron-scattering ͑INS͒ cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate 1/T 1 of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit TӶ⌬. The results for 1/T 1 are compared with the experimental findings of Takigawa et al. ͓Phys. Rev. Lett. 76, 2173 ͑1996͔͒ and the agreement is quite good. In the regime ⌬ϽTϽ͑a typical microscopic exchange͒ and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.

We present results on the low-frequency dynamical and transport properties of random quantum systems whose low temperature (T), low-energy behavior is controlled by strong-disorder fixed points. We obtain the momentum-and frequency-dependent dynamic structure factor in the random singlet ͑RS͒ phases of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the random dimer and Ising antiferromagnetic phases of spin-1/2 random antiferromagnetic chains. We show that the RS phases are unusual ''spin metals'' with divergent low-frequency spin conductivity at Tϭ0, and we also follow the conductivity through ''metal-insulator'' transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength of disorder in the spin-1 case. We work out the average spin and energy autocorrelations in the one-dimensional random transverse-field Ising model in the vicinity of its quantum critical point. All of the above calculations are valid in the frequency-dominated regime տT, and rely on previously available renormalization group schemes that describe these systems in terms of the properties of certain strong-disorder fixed-point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite ''hydrodynamic'' regime ϽT for the special case of spin-1/2 chains close to the planar limit ͑the quantum x-y model͒ by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.

We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states (E) at the band center Eϭ0. The most general system of this kind ͓R. Gade, Nucl. Phys. B 398, 499 ͑1993͔͒ exhibits critical behavior and has (E) that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. ͓Phys. Rev. B 50, 7526 ͑1994͔͒ has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder-this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ''surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is (E)ϳE Ϫ1 e Ϫc͉ln E͉ 2/3 , different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ''string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.

We study the physics of hard-core bosons with unfrustrated hopping (t) and nearest-neighbor repulsion (V) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small V/t superfluid state eventually becomes unstable at large enough V/t to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a U(1) lattice gauge theory, allowing us to identify this insulator with a U(1) fractionalized Mott-insulating state. The possibility of observing this phase in suitably designed atom-trap experiments with ultracold atoms is also discussed, as are specific experimental signatures.