arXiv subjects

Assa Auerbach

Publications and source records attributed to Assa Auerbach.

At least 37 records · Page 2Linked to original sources

arXiv2013

Dynamics and Conductivity Near Quantum Criticality

Relativistic O(N) field theories are studied near the quantum critical point in two space dimensions. We compute dynamical correlations by large scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For N=3 and 4 we confirm its ω^3 rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For N=2, the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons, (Josephson arrays) the power law rise above the Higgs mass, increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be σ^*_c = 0.3 (\pm 0.1) 4e^2/h. In the appendices, we describe a generalization of the worm algorithm to N>2, and also a singular value decomposition error analysis for the numerical analytic continuation.

cond-mat.str-el↗

arXiv2012

p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet

The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order parameter should split the optical phonons degeneracy near the zone center. Addition of weak next to nearest neighbor coupling is discussed.

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arXiv2012

Visibility of the Amplitude (Higgs) Mode in Condensed Matter

The amplitude mode is a ubiquitous collective excitation in condensed matter systems with broken continuous symmetry. It is expected in antiferromagnets, short coherence length superconductors, charge density waves, and lattice Bose condensates. Its detection is a valuable test of the corresponding field theory, and its mass gap measures the proximity to a quantum critical point. However, since the amplitude mode can decay into low-energy Goldstone modes, its experimental visibility has been questioned. Here we show that the visibility depends on the symmetry of the measured susceptibility. The longitudinal susceptibility diverges at low frequency as χ_{σσ} ~ i/ω(d=2) or log(1/|ω|) (d=3), which can completely obscure the amplitude peak. In contrast, the scalar susceptibility is suppressed by four extra powers of frequency, exposing the amplitude peak throughout the ordered phase. We discuss experimental setups for measuring the scalar susceptibility. The conductivity of the O(2) theory (relativistic superfluid) is a scalar response and therefore exhibits suppressed absorption below the Higgs mass threshold, σ~ ω^{2d+1}. In layered, short coherence length superconductors, (relevant e.g. to cuprates) this threshold is raised by the interlayer plasma frequency.

cond-mat.supr-con↗

arXiv2011

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, {\em 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 $n_{\rm svd}$ 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 $\exp(-n_{\rm svd}^{1/S_{ee}})$. Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.

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arXiv2011

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, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium 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 super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

cond-mat.mes-hall↗

arXiv2010

Vortex Dynamics and Hall Conductivity of Hard Core Bosons

Magneto-transport of hard core bosons (HCB) is studied using an XXZ quantum spin model representation, appropriately gauged on the torus to allow for an external magnetic field. We find strong lattice effects near half filling. An effective quantum mechanical description of the vortex degrees of freedom is derived. Using semiclassical and numerical analysis we compute the vortex hopping energy, which at half filling is close to magnitude of the boson hopping energy. The critical quantum melting density of the vortex lattice is estimated at 6.5x10-5 vortices per unit cell. The Hall conductance is computed from the Chern numbers of the low energy eigenstates. At zero temperature, it reverses sign abruptly at half filling. At precisely half filling, all eigenstates are doubly degenerate for any odd number of flux quanta. We prove the exact degeneracies on the torus by constructing an SU(2) algebra of point-group symmetries, associated with the center of vorticity. This result is interpreted as if each vortex carries an internal spin-half degree of freedom ('vspin'), which can manifest itself as a charge density modulation in its core. Our findings suggest interesting experimental implications for vortex motion of cold atoms in optical lattices, and magnet-transport of short coherence length superconductors.

cond-mat.supr-con↗

arXiv2009

"Bad Metal" Conductivity of Hard Core Bosons

Two dimensional hard core bosons suffer strong scattering in the high temperature resistive state at half filling. The dynamical conductivity is calculated using non perturbative tools such as continued fractions, series expansions and exact diagonalization. We find a large temperature range with linearly increasing resistivity and broad dynamical conductivity, signaling a breakdown of Boltzmann-Drude quasiparticle transport theory. At zero temperature, a high frequency peak in the dynamical conductivity appears above a "Higgs mass" gap, and corresponds to order parameter magnitude fluctuations. We discuss the apparent similarity between conductivity of hard core bosons and phenomenological characteristics of cuprates, including the universal scaling of Homes et. al. (Nature 430, 539 (2004)).

cond-mat.str-el↗

arXiv2009

Temperature Dependence Of Cuprate Superconductors' Order Parameter

A model of charged hole-pair bosons, with long range Coulomb interactions and very weak interlayer coupling, is used to calculate the order parameter -Phi- of underdoped cuprates. Model parameters are extracted from experimental superfluid densities and plasma frequencies. The temperature dependence -Phi(T)- is characterized by a 'trapezoidal' shape. At low temperatures, it declines slowly due to harmonic phase fluctuations which are suppressed by anisotropic plasma gaps. Above the single layer Berezinski-Kosterlitz-Thouless (BKT) temperature, Phi(T) falls rapidly toward the three dimensional transition temperature. The theoretical curves are compared to c-axis superfluid density data by H. Kitano et al., (J. Low Temp. Phys. 117, 1241 (1999)) and to the -transverse nodal velocity- measured by angular resolved photoemmission spectra on BSCCO samples by W.S. Lee et al., (Nature 450, 81 (2007)), and by A. Kanigel, et al., (Phys. Rev. Lett. 99, 157001 (2007)).

cond-mat.supr-con↗

arXiv2009

Majorana fermions of a two-dimensional Px+iPy superconductor

To investigate Majorana fermionic excitations of a $p_x+ip_y$ superconductor, the Bogoliubov-de-Gennes equation is solved on a sphere for two cases: (i) a vortex-antivortex pair at opposite poles and (ii) an edge near the south pole and an antivortex at the north pole. The vortex cores support a state of two Majorana fermions, the energy of which decreases exponentially with the radius of the sphere, independently of a moderate disorder potential. The tunneling conductance of an electron into the superconductor near the position of a vortex is computed for finite temperature, and is compared to the case of an {\it s}-wave superconductor. The zero bias conductance peak of the antivortex is half that of the vortex. This effect can be used as a probe of the order parameter symmetry, and as a direct measurement of the Majorana fermion.

cond-mat.supr-con↗

arXiv2009

Transport Studies of Lattice Bosons: Paradigms for Fluctuating Superconductivity

A strong periodic potential generally enhances the short wavelength fluctuations of a superfluid beyond the validity of standard continuum approaches. Here we report some recent results on hard core bosons on finite lattices. We find several interesting effects of the periodic potential on the ground state, vortex dynamics, and and Hall conductivity. For example, the Magnus field on a vortex abruptly reverses direction at half filling. A rotating Bose condensate on an optical lattice may allow an experimental test of our results. Insight may also be gained about strongly fluctuating superconductors modelled by charge 2e lattice bosons.

cond-mat.supr-con↗

arXiv2008

Testing for Majorana Zero Modes in a Px+iPy 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 $Δ^2/eF$. 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 $T >> Δ^2/eF$.

cond-mat.str-el↗

arXiv2008

Schwinger Bosons Approaches to Quantum Antiferromagnetism

These lectures review the large N Schwinger Bosons Mean Field approach to the quantum Heisenberg model. The method applies to ordered and disordered phases in all dimensions, at zero and at finite temperature. Extension to frustrated models is explained. An example for an experimentally useful application, is the temperature dependent staggered magnetization of the layered antiferromagnet.

cond-mat.str-el↗

arXiv2008

Emergence of Spin-Half Fermion Vortices and The Vortex Metal

This paper has been withdrawn and replaced by a new version entitled "Vortex quantum dynamics of two dimensional lattice bosons" By Netanel H. Lindner, Assa Auerbach, Daniel P. Arovas, posted in arXiv:0810.2604. The calculations and results of the original manuscript were correct, and lead to several important conclusions about vortex dynamics and Hall conductance. However, we have dropped our conjecture, that vortices exhibit mutual Fermi statistics. The conjecture was based on the antisymmetry under exchange of two vortices, as revealed in the lowest eight many-body eigenstates of 16 sites toroidal lattices. Appealing to an effective Harper bosons model on larger lattices, revealed vortex eigenstates with both Bose and Fermi permutation symmetries, although vortices do carry spin half quantum numbers. It may exemplify that a general non-relativistic "spin-statistics theorem" in two dimensions does not hold.

cond-mat.supr-con↗

arXiv2008

Vortex quantum dynamics of two dimensional lattice bosons

In two dimensions a vortex lattice can melt by quantum fluctuations into a non-superfluid Quantum Vortex Liquid (QVL). To determine the melting conditions, we compute the bare vortex hopping rate by exact diagonalization of square clusters near half filling. Mapping our effective Hamiltonian to the Boson Coloumb Liquid simulated in Phys. Rev. Lett. 73, 826 (1994), we expect a QVL above a melting density of 0.0065 vortices per lattice site. We also compute the Hall conductivity using adiabatic curvatures. As a function of boson filling it reverses sign at half filling in a sharp transition accompanied by a vanishing temperature scale. At half filling, each vortex carries a spin half quantum number (`v-spin'), as a consequence of local non commuting SU(2) symmetries. Implications of these results could be realized in cold atoms, Josephson junction arrays and cuprate superconductors.

cond-mat.supr-con↗

arXiv2007

Nonlinear Current of Strongly Irradiated Quantum Hall Gas

Two dimensional electrons in weakly disordered high Landau levels are considered. The current-field response in the presence of a strong microwave field, is computed. The disordered Floquet evolution operator allows us to treat the short range disorder perturbatively, at any strength of electric fields. A simplifying Random Matrix Approximation reproduces the broadened Landau levels density of states and structure factor. We derive the magnitude of the Microwave Induced Resistivity Oscillations. The disorder short wavelength cut-off determines the non-linear electric fields of the Zero Resistance State and the Hall Induced Resistivity Oscillations. We discuss wider implications of our results on experiments and other theories.

cond-mat.mes-hall↗

arXiv2006

A magnetic analog of the isotope effect in cuprates

We present extensive magnetic measurements of the (Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_{3}O_{y} (CLBLCO) system with its four different families (x) having a Tc^max(x) variation of 28% and minimal structural changes. For each family we measured the Neel temperature, the anisotropies of the magnetic interactions, and the spin glass temperature. Our results exhibit a universal relation Tc=c*J*n_s for all families, where c~1, J is the in plane Heisenberg exchange, and n_s is the carrier density. This relates cuprate superconductivity to magnetism in the same sense that phonon mediated superconductivity is related to atomic mass.

cond-mat.supr-con↗

arXiv2006

Vortex Tunneling and Transport Theory In Two-Dimensional Bose Condensates

The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy we argue that the -Hall conductivity- (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wavefunctions and overlap calculations, and a general derivation of the Magnus coefficient for any wavefunction on the sphere, are provided in appendices.

cond-mat.supr-con↗

arXiv2005

Domain Patterns in the Microwave-Induced Zero-Resistance State

It has been proposed that the microwave-induced ``zero-resistance'' phenomenon, observed in a GaAs two-dimensional electron system at low temperatures in moderate magnetic fields, results from a state with multiple domains, in which a large local electric field $\bE(\br)$ is oriented in different directions. We explore here the questions of what may determine the domain arrangement in a given sample, what do the domains look like in representative cases, and what may be the consequences of domain-wall localization on the macroscopic dc conductance. We consider both effects of sample boundaries and effects of disorder, in a simple model, which has a constant Hall conductivity, and is characterized by a Lyapunov functional.

cond-mat.mes-hall↗