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 hard-core bosons with unfrustrated hopping (t) and nearest neighbour repulsion (U ) on the triangular lattice. At half-filling, the system undergoes a zero temperature (T ) quantum phase transition from a superfluid phase at small U to a supersolid at Uc ≈ 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic √ 3 × √ 3 pattern, and is remarkably stable-indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t. Introduction: The observation of strongly correlated Mott insulating states and T = 0 superfluid-insulator transitions of ultracold bosonic atoms subjected to optical lattice potentials 1 has led to a great deal of interest in strongly correlated lattice systems that can be realized in such experiments.2,3 The recent observation of a supersolid phase in Helium 4 leads, in this context, to a natural question: Can the lattice analog of this, namely a superfluid phase that simultaneously breaks lattice translation symmetry, be seen in atom-trap experiments?One class of promising candidates are systems which are superfluid when interactions are weak, but form insulators with spatial symmetry breaking when interactions are strong: In terms of conventional Landau theory, a direct transition between these two states is generically either first order, or pre-empted by an intermediate supersolid phase with both order parameters nonzero; both types of behaviour are known to occur in specific lattice models.5,6,7 Moreover, as has been shown recently by Senthil et. al., 8 conventional Landau theory can fail in certain situations in which quantum mechanical Berry phase effects produce a direct second-order phase transition, thereby ruling out an intermediate supersolid phase. When such a transition occurs, 9,10 it is associated with quasi-particle fractionalization and deconfinement, and this alternative to an intermediate supersolid phase is thus interesting in its own right.Bosons on the triangular lattice with on-site repulsion V , repulsive nearest neighbour interaction U , and unfrustrated hopping (t) provide a particularly interesting example in this context since the structure of interactions is simple enough that it can be realized in atom-trap experiments.2,11 In the hard-core V → ∞ limit (which is also experimentally feasible 2,11 ) this maps to a system of S = 1/2 spins (S

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.

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum O(3) non-linear σ-model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.Over the past decade, a large number of onedimensional, insulating, Heisenberg antiferromagnets with a zero temperature (T ) spin gap have been studied: these include integer spin chains 1,2 and half-integer spin-ladder systems 3 . In the large spin S limit, the low energy properties of these compounds are described 4 by the one-dimensional quantum O(3) non-linear σ-model (without any topological term), and there is evidence 5 that the mapping to this continuum model is quantitatively accurate even for the S = 1 spin chain. Theoretically, much is known about the quantum field theory of the σ-model 6-8 , and this information has been valuable in understanding the properties of the spin chains. The low energy spectrum of the σ-model consists of a triplet of massive particles, and their ballistic propagation describes many exactly known dynamic correlations at T = 0. For T > 0 however, exact results have so far been limited to static, thermodynamic observables 9 . In this paper, we obtain dynamic, non-zero T correlators using a semiclassical method 11 : we claim that all of our results are asymptotically exact at low T , but this has not been rigorously established. We present universal functions which describe the crossover from ballistic spin transport at short scales, to diffusive behavior at the longest scales; as a bi-product, these functions yield the exact value of the spin diffusion constant. The nature of spin transport for any small T > 0 is therefore qualitatively different from that at T = 0.The imaginary time (τ ) action of the σ-model is

We study the approach to equilibrium of a Bose gas to a superfluid state. We point out that dynamic scaling, characteristic of far from equilibrium phaseordering systems, should hold. We stress the importance of a non-dissipative Josephson precession term in driving the system to a new universality class. non-equilibrium phenomena in a heretofore inaccessible regime. In particular, an issue which could be experimentally investigated, and which we shall address theoretically in this paper is the following-upon quenching a Bose gas to a final temperature (T ) below T c , how does the condensate density grow with time before attaining its final equilibrium value? A few recent papers [3,4] have addressed just this question, but they have focussed on the early time (on the order of a few collision times), non-universal dynamics. However, as has also been noted recently in Ref [5], the interesting experimental questions are instead associated with the long-time dynamics involving the coarsening of the Bose condensate order parameter. This dynamics is "universal" in a sense that will be clarified below.A natural and precise language for describing the evolution of the condensate is offered by recent developments in the theory of phase-ordering dynamics in dissipative classical spin systems, as reviewed in the article by Bray [6]. In this theory, one considers the evolution of a classical spin system after a rapid quench from some high T to a low T in the ordered phase.The dynamics is assumed to be purely relaxational, and each spin simply moves along the steepest downhill direction in its instantaneous energy landscape. Locally ordered regions will appear immediately after the quench, but the orientation of the spins in each region will be different. The coarsening process is then one of alignment of neighboring regions, usually controlled by the motion and annihilation of defects (domain walls for Ising spins, vortices for XY spins etc.). A key step in the theory is the introduction of a single length scale, l(t), a monotonically increasing function of the time t, which is about the size of a typical ordered domain at time t. Provided l(t) is greater than microscopic length scales, like the range of interactions or the lattice spacing, it is believed that the late stage morphology of the system is completely characterized by l(t), and is independent of microscopic details, i.e. it is universal. This morphology is characterized by various time dependent correlation functions which exhibit universal scaling behavior.We turn then to the Bose gas. The order parameter in this case is the boson annihilation