Two-dimensional frustrated Heisenberg model: Variational study

The stability of the ferromagnetic phase of the 2D quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnon are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function of new type. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain the accurate estimate of the transition point and to study the character of the phase transition.Comment: 10 pages, 4 figures, RevTe

An exactly solvable model of the BCS-BEC crossover

We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.Comment: corrected typos, minor modifications, submitted versio

A layering model for superconductivity in the borocarbides

We propose a superlattice model to describe superconductivity in layered materials, such as the borocarbide families with the chemical formul\ae\ $RT_2$B$_2$C and $RT$BC, with $R$ being (essentially) a rare earth, and $T$ a transition metal. We assume a single band in which electrons feel a local attractive interaction (negative Hubbard-$U$) on sites representing the $T$B layers, while U=0 on sites representing the $R$C layers; the multi-band structure is taken into account minimally through a band offset $\epsilon$. The one-dimensional model is studied numerically through the calculation of the charge gap, the Drude weight, and of the pairing correlation function. A comparison with the available information on the nature of the electronic ground state (metallic or superconducting) indicates that the model provides a systematic parametrization of the whole borocarbide family.Comment: 4 figure

Density of Neutral Solitons in Weakly Disordered Peierls Chains

We study the effects of weak off-diagonal disorder on Peierls systems with a doubly degenerate ground state. We show that for these systems disorder in the electron hopping amplitudes induces a finite density of solitons in the minimal-energy lattice configuration of a single chain. These disorder-induced dimerization kinks are neutral and have spin 1/2. Using a continuum model for the Peierls chain and treating the lattice classically, we analytically calculate the average free energy and density of kinks. We compare these results to numerical calculations for a discrete model and discuss the implications of the kinks for the optical and magnetic properties of the conjugated polymer trans-polyacetylene.Comment: 28 pages, revtex, 5 Postscript figures, to appear in Phys. Rev.

Superconductivity in an exactly solvable Hubbard model with bond-charge interaction

The Hubbard model with an additional bond-charge interaction $X$ is solved exactly in one dimension for the case $t=X$ where $t$ is the hopping amplitude. In this case the number of doubly occupied sites is conserved. In the sector with no double occupations the model reduces to the $U=\infty$ Hubbard model. In arbitrary dimensions the qualitative form of the phase diagram is obtained. It is shown that for moderate Hubbard interactions $U$ the model has superconducting ground states.Comment: Revtex, 14 pages, 1 figure (uuencoded compressed tar-file

Theory of ultracold Fermi gases

The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, of the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to non-perturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare the theoretical predictions with the available experimental results.Comment: Revised and abridged version accepted for publication in Rev. Mod. Phys.: 63 pages, 36 figure

Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

[[abstract]]The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U 0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n. It is found that the spin susceptibility at half- filling is non-analytic and changes discontinuously asU → 0. The exact theory shows the absence of a charge energy gap in the U 0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.[[journaltype]]國外[[booktype]]紙本[[countrycodes]]GB