Local density approximation for a perturbative equation of state

The knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic ``perturbative'' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size and density profile of a trapped system in three-, two-, and one- dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. Physical meaning of expansion terms in a number of systems is discussed.Comment: 3 Figure

Quasi-one-dimensional anisotropic Heisenberg model in a transverse magnetic field

The phase diagram of weakly coupled $XXZ$ chains in a transverse magnetic field is studied using the mean-field approximation for the interchain coupling and known exact results for an effective one-dimensional model. Results are applied to the quasi-one-dimensional antiferromagnet $Cs_{2}CoCl_{4}$ and the value of interchain interaction in this compound is estimated.Comment: 4 pages, 2 figure

Gap generation in the XXZ model in a transverse magnetic field

The ground state phase diagram of the 1D XXZ model in transverse magnetic field is obtained. It consists of the gapped phases with different types of long range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of all critical lines.Comment: 4 pages, 1 figure, Late

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

Frustrated quantum Heisenberg ferrimagnetic chains

We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest and next-nearest neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S_1 > S_2, using 1/S spin-wave expansions, density-matrix renormalization group, and exact- diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate- incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.Comment: 16 pages (LaTex 2.09), 6 eps figure

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