Degeneracy-Projected Polarization Formulas for Hall-Type Conductivities.

Kubo formulas for Hall, transverse thermoelectric, and thermal Hall conductivities are simplified into on-shell commutators of degeneracy projected polarizations. The new expressions are computationally economical, and apply to general Hamiltonians without a gap restriction. We show that Hall currents in open boundaries are carried by gapless chiral excitations.

Hall Coefficient of Semimetals.

A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev.

Hall Number of Strongly Correlated Metals.

An exact formula for the temperature dependent Hall number of metals is derived. It is valid for nonrelativistic fermions or bosons, with an arbitrary potential and interaction. This dc transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity.

Doped Kondo chain, a heavy Luttinger liquid.

The doped 1D Kondo Lattice describes complex competition between itinerant and magnetic ordering. The numerically computed wave vector-dependent charge and spin susceptibilities give insights into its low-energy properties. Similar to the prediction of the large N approximation, gapless spin and charge modes appear at the large Fermi wave vector.

Nonlinear Conductivity and Collective Charge Excitations in the Lowest Landau Level.

For weakly disordered fractional quantum Hall phases, the nonlinear photoconductivity is related to the charge susceptibility of the clean system by a Floquet boost. Thus, it may be possible to probe collective charge modes at finite wave vectors by electrical transport. Incompressible phases, irradiated at slightly above the magnetoroton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields.

Collective Modes in a Quantum Solid.

We provide a theoretical explanation for the optical modes observed in inelastic neutron scattering on the bcc solid phase of helium 4 [T. Markovich et al., Phys.

Critical capacitance and charge-vortex duality near the superfluid-to-insulator transition.

Using a generalized reciprocity relation between charge and vortex conductivities at complex frequencies in two space dimensions, we identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We compute the ratio of boson superfluid stiffness to vortex condensate stiffness at mirror points to be 0.21(1) for the relativistic O(2) model.

Fate of the Higgs mode near quantum criticality.

We study a relativistic O(N) model near the quantum critical point in 2 + 1 dimensions for N = 2 and N = 3. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a well-defined peak associated with the Higgs mode arbitrarily close to the critical point.

Floquet spectrum and transport through an irradiated graphene ribbon.

Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region.

Reducing memory cost of exact diagonalization using singular value decomposition.

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, without restricting to variational ansatzes. The lattice of size N is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of n(svd) smaller subcluster vectors using singular value decomposition.

Testing for majorana zero modes in a p(x) + ip(y) superconductor at high temperature by tunneling spectroscopy.

Directly observing a zero energy Majorana state in the vortex core of a chiral superconductor by tunneling spectroscopy requires energy resolution better than the spacing between core states delta0(2)/epsilon F. We show that, nevertheless, its existence can be decisively tested by comparing the temperature-broadened tunneling conductance of a vortex with that of an antivortex even at temperatures T >> delta0(2)/epsilon F.

Vortex quantum dynamics of two dimensional lattice bosons.

We study hard-core lattice bosons in a magnetic field near half filling. The bare vortex hopping rate is extracted from exact diagonalizations of square clusters. We deduce a quantum melting of the vortex lattice above vortex density of 6.

Steady states of a microwave-irradiated quantum-Hall gas.

We consider effects of a long-wavelength disorder potential on the zero conductance state (ZCS) of the microwave-irradiated 2D electron gas. Assuming a uniform Hall conductivity, we construct a Lyapunov functional and derive stability conditions on the domain structure of the photogenerated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find nonzero conductances, photovoltages, and circulating dissipative currents.

Low-energy singlets in the Heisenberg antiferromagnet on the kagomé lattice.

The spin-1/2 Heisenberg antiferromagnet on the kagomé lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale.

Singlet excitations in pyrochlore: a study of quantum frustration.

We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet on the frustrated checkerboard and pyrochlore lattices. Their ground states are spin-gapped singlets which break lattice symmetry. Their effective Hamiltonians describe fluctuations of orthogonal singlet pairs on tetrahedral blocks, at an emergent low energy scale.

Luttinger-liquid behavior in tunneling through a quantum dot at zero magnetic field.

Thermodynamic and transport properties of a two-dimensional circular quantum dot are studied theoretically at zero magnetic field. In the limit of a large confining potential, where the dot spectrum exhibits a shell structure, it is argued that both spectral and transport properties should exhibit Luttinger liquid behavior. These predictions are verified by direct numerical diagonalization.

Oscillating superfluidity of bosons in optical lattices.

Following a suggestion by Orzel et al. [Science 291, 2386 (2001)]], we analyze bosons in an optical lattice undergoing a sudden parameter change from the Mott to superfluid phase. We introduce a modified coherent states path integral to describe both phases.