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. Extrapolation of finite lattice calculations to the dc-thermodynamic limit is demonstrated for a disordered metal.

Hall Coefficient of Semimetals.

A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 066601 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.066601] is applied to nodal line and Weyl semimetals (including graphene) and to spin-orbit split semiconductor bands in two and three dimensions. The calculation reduces to a ratio of two equilibrium susceptibilities, where corrections are negligible at weak disorder. Deviations from Drude's inverse carrier density are associated with band degeneracies, Fermi surface topology, and interband currents. Experiments which can measure these deviations are proposed.

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. The highly suppressed spin velocity is a manifestation of "heavy" Luttinger liquid quasiparticles. A low-energy hybridization gap is detected at the small (conduction band) Fermi wave vector. In contrast to the exponential suppression of the Fermi velocity in the large-N approximation, we fit the spin velocity by a density-dependent power law of the Kondo coupling. The differences between the large-N theory and our numerical results are associated with the emergent magnetic Ruderman-Kittel-Kasuya-Yosida interactions.

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. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.

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. Nonlinear conductivity can probe composite fermions' charge excitations in compressible filling factors.

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. Rev. Lett. 88, 195301 (2002)]. We argue that these excitations are amplitude (Higgs) modes associated with fluctuations of the crystal order parameter within the unit cell. We present an analysis of the modes based on an effective Ginzburg-Landau model, classify them according to their symmetry properties, and compute their signature in inelastic neutron scattering experiments. In addition, we calculate the dynamical structure factor by means of an ab intio quantum Monte Carlo simulation and find a finite frequency excitation at zero relative momentum.

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. The product of dynamical conductivities at mirror points is used as a quantitative measure of deviations from self-duality between charge and vortex theories. We propose the finite wave vector compressibility as an experimental measure of the vortex condensate stiffness for neutral lattice bosons.

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. The peak fidelity and the amplitude ratio between the critical energy scales on both sides of the transition are determined.

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. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk dc conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

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. For low entanglement entropy S(ee), (satisfied by short-range Hamiltonians), the truncation error is expected to vanish as exp(-n(svd)(1/S(ee))). Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30, and 36 sites, with no lattice symmetries exploited, using less than 15 GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.

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 6.5x10(-3) per lattice site. The Hall conductivity reverses sign abruptly as the density crosses half filling, where its characteristic temperature scale vanishes. We prove that at precisely half filling, each vortex carries a spin-1/2 quantum number ("v spin"). Experimental implications of these results are discussed.

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.

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. In contrast, weak white-noise disorder does not destroy the ZCS, but induces mesoscopic current fluctuations.

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. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. We calculate its damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.

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. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic T2 specific heat observed experimentally.

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. The experimental implications of such Luttinger liquid characteristics are discussed.

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. We discuss low temperature thermodynamics and new interpretations of finite size numerical data. We argue that our results are common to many models of quantum frustration.