Kedar Damle

NONZERO-TEMPERATURE TRANSPORT NEAR QUANTUM CRITICAL POINTS

We describe the nature of charge transport at non-zero temperatures (T ) above the two-dimensional (d) superuid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order kBT=h. This implies that the transport at frequencies ! kBT=h is in the hydrodynamic, collision-dominated (or ‘incoherent’) regime, while ! kBT=h is the collisionless (or ‘phasecoherent’) regime. The conductivity is argued to be e 2 =h times a non-trivial universal scaling function ofh!=kBT , and not independent of h!=kBT ,a s has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic h!=kBT ! 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 collisionless h!=kBT !1limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a dierent universal number times e 2 =h. We provide the rst 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 =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.

Persistent Supersolid Phase of Hard-Core Bosons on the Triangular Lattice

We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) 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 approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.

SPIN DYNAMICS AND TRANSPORT IN GAPPED ONE-DIMENSIONAL HEISENBERG ANTIFERROMAGNETS AT NONZERO TEMPERATURES

We present the theory of nonzero temperature (T ) spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with an energy gap . For T , we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particleS-matrix which has a super-universal 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 representation) for the two-leg S =1 =2 Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals aS =1 , two particle bound state which leads to the presence of a second peak in the T =0 inelastic neutron scattering (INS) cross-section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasi-particle peak in the INS cross-section, for the magnetization transport, and for the eld dependence of the NMR relaxation rate 1=T1 of the eective semiclassical model: these are expected to be asymptotically exact for the quantum antiferromagnets. The results for 1=T1 are compared with the experimental ndings of Takigawa et.al. and the agreement is quite good. In the regime < T <(a typical microscopic exchange) we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.

LOW TEMPERATURE SPIN DIFFUSION IN THE ONE-DIMENSIONAL QUANTUM O (3) NONLINEAR Q MODEL

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum

Dynamics and transport in random quantum systems governed by strong-randomness fixed points

\mathrm{O}(3)

Unusual liquid state of hard-core bosons on the pyrochlore lattice.

nonlinear

Particle-hole symmetric localization in two dimensions

\ensuremath{\sigma}

PHASE ORDERING KINETICS OF THE BOSE GAS

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.

PHASE TRANSITION OF A BOSE GAS IN A HARMONIC POTENTIAL

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 (RS) 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 T=0, 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 ω≳T, 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 ω<T for the special case of spin-1/2 chains close to the planar limit (the quantum x-y model) by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.

Impurity spin texture at a deconfined quantum critical point

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.