arXiv subjects

Assa Auerbach

Publications and source records attributed to Assa Auerbach.

64 records · Page 4Linked to original sources

arXiv1996

Superfluids and Supersolids on Frustrated 2D Lattices

We study the ground state of hard-core bosons with nearest-neighbor hopping and nearest-neighbor interactions on the triangular and Kagomé lattices by mapping to a system of spins ($S={1\over2}$), which we analyze using spin-wave theory. We find that the both lattices display superfluid and supersolid (a coexistence of superfluid and solid) order as the parameters and filling are varied. Quantum fluctuations seem large enough in the Kagomé system to raise the interesting possibility of a disordered ground state.

cond-mat↗

arXiv1996

The Quantized Hall Insulator

We model the insulator neighboring the 1/k quantum Hall phase by a random network of puddles of filling fraction 1/k. The puddles are coupled by weak tunnel barriers. Using Kirchoff's laws we prove that the macroscopic Hall resistivity is quantized at $k h/ e^2$ and independent of magnetic field and current bias -- in agreement with recent experimental observations. In addition, for k>1 this theory predicts non linear longitudinal response $V\sim I^α$ at zero temperature, and $V/I\sim T^{1-{1\over α}}$ at low bias. $α$ is determined using Renn and Arovas' theory for the single junction response, and is related to the Luttinger liquid spectra of the edge states straddling the typical tunnel barrier. The dependence of $V(I)$ on the magnetic field is related to the typical puddle size. Deviations of $V(I)$ from a pure power law are estimated using a series/parallel approximation for the two dimensional random nonlinear resistor network. We check the validity of this approximation by numerically solving for a finite square lattice network.

cond-mat↗

arXiv1995

TDAE-\c60: Can a Mott insulator be a ferromagnet?

Motivated by the structure of TDAE-\c60, we derive a multicomponent superexchange Hamiltonian for the spins and orbital (``isospin'') degrees of freedom in the Mott-insulating phase. We explore its phase diagram and identify points of special interest: an SU(4) antiferromagnet (solved by Sutherland) and two ferromagnet$\otimes$antiferromagnet points where the ground state is known. For the ferromagnetic regime, we apply interchain mean field theory and derive an expression for the Curie temperature where spin ordering occurs and a lower Ne{é}l temperature for a conjectured isospin ordering.

cond-mat↗

arXiv1994

Electron--Vibron Interactions and Berry Phases in Charged Buckminsterfullerene: Part I

A simple model for electron-vibron interactions on charged buckminsterfullerene C$_{60}^{n-}$, $n=1,\ldots 5$, is solved both at weak and strong couplings. We consider a single $H_g$ vibrational multiplet interacting with $t_{1u}$ electrons. At strong coupling the semiclassical dynamical Jahn-Teller theory is valid. The Jahn-Teller distortions are unimodal for $n$=1,2,4,5 electrons, and bimodal for 3 electrons. The distortions are quantized as rigid body pseudo--rotators which are subject to geometrical Berry phases. These impose ground state degeneracies and dramatically change zero point energies. Exact diagonalization shows that the semiclassical level degeneracies and ordering survive well into the weak coupling regime. At weak coupling, we discover an enhancement factor of $5/2$ for the pair binding energies over their classical values. This has potentially important implications for superconductivity in fullerides, and demonstrates the shortcoming of Migdal--Eliashberg theory for molecular crystals.

cond-mat↗

arXiv1994

Electron--Vibron Interactions in Charged Buckminsterfullerene: Pair Energies and Spectra (Part II)

The ground state energy shifts and excitation spectra of charged buckminsterfullerene C$_{60}^{n-}$, $n=1,\ldots 5$ are calculated. The electron--vibron Hamiltonian of Part I is extended to include all $A_g$ and $H_g$ modes with experimentally determined frequencies and theoretically estimated coupling constants. Complex splitting patterns of $H_g$ vibrational levels are found. Our results are relevant to EPR measurements of spin splittings in C$_{60}^{2-}$ and C$_{60}^{3-}$ in solution. Spectroscopic gas-phase experiments will be of interest for further testing of this theory. As found in Part I, degeneracies in the electron and vibron Hamiltonians give rise to a dynamical Jahn Teller effect, and to a considerable enhancement of the electronic pairing interaction. This helps to overcome repulsive Coulomb interactions and has important implications for superconductivity in K$_3$C$_{60}$ and the insulating state in K$_4$C$_{60}$.

cond-mat↗

arXiv1993

Vibrations and Berry Phases of Charged Buckminsterfullerene

A simple model of electron-vibron interactions in buckminsterfullerene ions is solved semiclassically. Electronic degeneracies of C$_{60}$$^{n-}$ induce dynamical Jahn-Teller distortions, which are unimodal for $n\!\ne\!3$ and bimodal for $n\!=\!3$. The quantization of motion along the Jahn-Teller manifold leads to a symmetric-top rotator Hamiltonian. I find Molecular Aharonov-Bohm effects where electronic Berry phases determine the vibrational spectra, zero point fluctuations, and electrons' pair binding energies. The latter are relevant to superconductivity in alkali-fullerenes.

cond-mat↗

arXiv1993

The Semiclassical Expansion of the t-J model

The Semiclassical Expansion of the t-J model. Lectures in the Jerusalem Winter School on Strongly Correlated Electrons, Dec. 1991, by Assa Auerbach, Physics Dept., Technion, Israel. LateX. Tech-102.

cond-mat↗

arXiv1993

The 1/N Expansion and Long Range Antiferromagnetic Order

The staggered magnetization of the Heisenberg antiferromagnet in two dimensions can be systematically approximated by a 1/N expansion. Cancellation between self energy diagrams leads to a Luttinger-like theorem for the ground state. We prove (for a smooth enough self energy) that the long range order of mean field theory ($N$=$\infty$) survives corrections to all orders of 1/N. Divergences of this series provides a new route to the disordered phases of quantum antiferromagnets.

cond-mat↗

arXiv1992

The $1/N$ Expansion and Spin Correlations in Constrained Wavefunctions

We develop a large-N expansion for Gutzwiller projected spin states. We consider valence bonds singlets, constructed by Schwinger bosons or fermions, which are variational ground states for quantum antiferromagnets. This expansion is simpler than the familiar expansions of the quantum Heisenberg model, and thus more instructive. The diagrammatic rules of this expansion allow us to prove certain identities to all orders in 1/N. We derive the on-site spin fluctuations sum rule for arbitrary N. We calculate the correlations of the one dimensional Valence Bonds Solid states and the Gutzwiller Projected Fermi Gas upto order 1/N. For the bosons case, we are surprised to find that the mean field, the order 1/N and the exact correlations are simply proportional. For the fermions case, the 1/N correction enhances the zone edge singularity. The comparison of our leading order terms to known results for N=2, enhances our understanding of large-N approximations in general.

cond-mat↗

arXiv1992

Spin Tunneling, Berry phases and Doped Antiferromagnets

Interference effects between Berry phase factors in spin tunneling systems have been discussed in recent Letters by Loss, DiVincenzo and Grinstein and von Delft and Henley. This Comment points out that Berry phases in spin tunneling are important in another interesting case: the two dimensional doped antiferromagnet. I show that the dispersion of a single hole in the t-J model changes sign as $e^{2πs}$ where $s$ is the size of the spins. This provides an interpretation of the numerical results for the $s=\half$ model, and a prediction for other spin sizes.

cond-mat↗