arXiv subjects

Assa Auerbach

Publications and source records attributed to Assa Auerbach.

At least 55 records · Page 3Linked to original sources

arXiv2005

Computing Effective Hamiltonians of Doped and Frustrated Antiferromagnets By Contractor Renormalization

A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high-Tc cuprates. For the S=1/2 Pyrochlore and Kagome antiferromagnets, the effective hamiltonians predict spin-disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.

cond-mat.str-el↗

arXiv2005

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 photo-generated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find non-zero conductances, photo-voltages, and circulating dissipative currents. In contrast, weak white noise disorder does not destroy the ZCS, but induces mesoscopic current fluctuations.

cond-mat.mes-hall↗

arXiv2004

Low Energy Singlets in the Heisenberg Kagome Antiferromagnet

The spin half Heisenberg antiferromagnet on the Kagome 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 non magnetic T-squared specific heat observed experimentally.

cond-mat.str-el↗

arXiv2003

Oscillating Superfluidity of Bosons in Optical Lattices

We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386 (2001), whereby bosons in an optical lattice would be subjected to a sudden parameter change from the Mott to the superfluid phase. We analyze the Bose Hubbard model with a modified coherent states path integral which can escribe - both - phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. These would be seen in time resolved interference patterns made by the released gas. We calculate the collective oscillation's 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.

cond-mat.soft↗

arXiv2002

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.

cond-mat.mes-hall↗

arXiv2002

Singlet Excitations in Pyrochlore: A Study of Quantum Frustration

The highly frustrated Heisenberg antiferromagnet on Checkerboard and Pyrochlore lattices is subject to strong quantum fluctuations. This problem is amenable to the Contractor Renormalization (CORE) algorithm, which systematically computes the effective interactions in a basis of local cluster eigenstates. CORE was recently used to derive the Plaquette Boson-Fermion model for the square lattice Hubbard model (cond-mat/0108087). For the spin half Checkerboard and Pyrochlore cases, we find singlet ground states which break lattice symmetry, and a gap to spin one excitations. The low excitations are singlets, coupled by Ising like interactions at an emergent low energy scale, which for the Pyrochlore is about 1% of the Heisenberg exchange. 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.

cond-mat.str-el↗

arXiv2002

Plaquette Boson-Fermion Model of Cuprates

The strongly interacting Hubbard model on the square lattice is reduced to the low energy Plaquette Boson Fermion Model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We apply the Contractor Renormalization method of Morningstar and Weinstein to compute the boson effective interactions. The range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. With hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons, the PBFM yields several testable predictions for photoemmission, tunneling asymmetry and entropy measurements.

cond-mat.supr-con↗

arXiv2000

Projected SO(5) Hamiltonian for Cuprates and Its Applications

The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and superconducting fluctuations of underdoped cuprates in terms of four bosons moving on a coarse grained lattice. A simple mean field approximation can explain some key feautures of the experimental phase diagram: (i) The Mott transition between antiferromagnet and superconductor, (ii) The increase of T_c and superfluid stiffness with hole concentration x and (iii) The increase of antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase. We apply this theory to explain the ``two gaps'' problem found in underdoped cuprate Superconductor-Normal- Superconductor junctions. In particular we explain the sharp subgap Andreev peaks of the differential resistance, as signatures of the antiferromagnetic resonance (the magnon mass gap). A critical test of this theory is proposed. The tunneling charge, as measured by shot noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather than by Delta Q=e as in conventional superconductors.

cond-mat.str-el↗

arXiv2000

Andreev Peaks and Massive Magnons in Cuprate SNS junctions

The projected SO(5) theory (pSO(5)) is used to resolve the puzzle of two distinct energy gaps in high T$_c$ Superconductor-Normal-Superconductor junctions. Counter to conventional theory of multiple Andreev reflections (MAR), the differential resistance peaks are associated with the antiferromagnetic resonance observed in neutron scattering, and not with Cooper pair breaking. The pSO(5) and MAR theories differ by the expected tunneling charges at the peaks. We propose that shot noise experiments could discriminate against the conventional interpretation.

cond-mat.supr-con↗

arXiv2000

Correlations in doped Antiferromagnets

A comprehensive study of doped RVB states is performed. It reveals a fundamental connection between superconductivity and quantum spin fluctuations in underdoped cuprates : {\em Cooper pair hopping} strongly reduces the local magnetization $m_0$. This effect pertains to recent muon spin rotation measurements in which $m_0$ varies weakly with hole doping in the poorly conducting regime, but drops precipitously above the onset of superconductivity. Gutzwiller mean field Approximation (GA) is found to agree with numerical Monte Carlo calculation. GA shows for example that for a bond amplitude $u(r)=e^{-r/ξ}$, spin spin correlations decay exponentially with a correlation length $\propto e^{3πξ^2/2}$. Expectation value of the Heisenberg model is found to be correlated with average loop density.

cond-mat.str-el↗

arXiv1999

Coulomb interactions and delocalization in quantum Hall constrictions

We study a geometry-dependent effect of long-range Coulomb interactions on quantum Hall (QH) tunneling junctions. In an X-shaped geometry, duality relates junctions with opening angles alpha and (pi - alpha). We prove that duality between weak tunneling and weak backscattering survives in the presence of long range interactions, and that their effects are precisely cancelled in the self dual geometry alpha=pi/2. Tunneling exponents as a function of alpha, the interaction strength chi, and the filling fraction nu are calculated. We find that Coulomb interaction induces localization in narrow channels (large alpha), and delocalization for sharply pinched constrictions (small alpha). Consequently, an insulator to metal transition happens at an angle alpha_c(chi,nu) <=pi/2. We discuss the implications of our results for tunneling experiments in QH-constriction and cleaved-edge geometries.

cond-mat.mes-hall↗

arXiv1999

Projected SO(5) Models

We construct a class of projected SO(5) models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO(5) symmetry where all static correlation functions are exactly SO(5) symmetric and discuss the signature of the projected SO(5) symmetry in dynamical correlation functions. We show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high T_c superconductors and account for many of their physical properties.

cond-mat↗

arXiv1999

Superconductivity and Quantum Spin Disorder in Cuprates

A fundamental connection between superconductivity and quantum spin fluctuations in underdoped cuprates, is revealed. A variational calculation shows that {\em Cooper pair hopping} strongly reduces the local magnetization $m_0$. This effect pertains to recent neutron scattering and muon spin rotation measurements in which $m_0$ varies weakly with hole doping in the poorly conducting regime, but drops precipitously above the onset of superconductivity.

cond-mat.str-el↗

arXiv1998

Hall Resistivity and Dephasing in the Quantum Hall Insulator

The longstanding problem of the Hall resistivity rho(x,y) in the Hall insulator phase is addressed using four-lead Chalker-Coddington networks. Electron interaction effects are introduced via a finite dephasing length. In the quantum coherent regime, we find that rho(x,y) scales with the longitudinal resistivity rho(x,x), and they both diverge exponentially with dephasing length. In the Ohmic limit, (dephasing length shorter than Hall puddles' size), rho(x,y) remains quantized and independent of rho(x,x). This suggests a new experimental probe for dephasing processes.

cond-mat.mes-hall↗

arXiv1998

Haldane Gap and Fractional Oscillations in Gated Josephson Arrays

An analogy between the twisted quantum xxz model and a gated Josephson junction array is used to predict sharp structure in the critical currents versus gate voltage, and fractional AC Josephson frequencies. We prove selection rules for level crossings which imply fractional periodicities of ground states with varying Aharonov-Bohm flux. Extrapolated numerical diagonalization on ladders, find a Haldane gap at moderate easy-plane anisotropy, with vanishing superfluid stiffness. Physical parameters for experimental realization of these novel effects are proposed.

cond-mat.supr-con↗

arXiv1997

Transport Through Quantum Melts

We discuss superconductor to insulator and quantum Hall transitions which are first order in the clean limit. Disorder creates a nearly percolating network of the minority phase. Electrical transport is dominated by tunneling or activation through the saddle point junctions, whose typical resistance is calculated as a function of magnetic field. In the Boltzmann regime, this approach yields resistivity laws which agree with recent experiments in both classes of systems. We discuss the origin of dissipation at zero temperature.

cond-mat.mes-hall↗

arXiv1997

Which tunnel faster across a quantum Hall strip: fractional charges or electrons?

The tunneling rate of fractional charge across a Laughlin state on the cylinder is computed numerically. The decay with strip width Y is fitted to exp[- a (Y/ l)**2/12] where l is the Landau length, and a is approximately 1.0. This rate is exponentially LARGER than the electron tunneling rate and can be interpreted by analogy to a superfluid vortex tunneling problem. Experimental implications include the ``law of corresponding states'', periodicity of Aharonov-Bohm resistance oscillations and charge measurements by quantum shot noise.

cond-mat.mes-hall↗

arXiv1996

Electronic Properties Of Buckminsterfullerenes: Degeneracies and Surprises

Buckminsterfullerene compounds exibit remarkable physics at low temperatures, e.g. high temperature superconductivity in alkali-fullerenes, and ferromagnetism in TDAE -C60. Here we review recent theoretical studies of electron correlations in these compounds. In particular, we discuss models of electron-vibron interactions, electron-electron interactions, and intermolecular hopping. We show that the origin of novel electronic phases lies in {\em local} degeneracies of C60; a direct consequence of the high molecular symmetry.

cond-mat.str-el↗