Flow Equations and Normal Ordering

In this paper we consider flow-equations where we allow a normal ordering which is adjusted to the one-particle energy of the Hamiltonian. We show that this flow converges nearly always to the stable phase. Starting out from the symmetric Hamiltonian and symmetry-broken normal ordering nearly always yields symmetry breaking below the critical temperature.Comment: 7 page

Possible Phases of the Two-Dimensional t-t' Hubbard Model

We present a stability analysis of the 2D t-t' Hubbard model on a square lattice for various values of the next-nearest-neighbor hopping t' and electron concentration. Using the free energy expression, derived by means of the flow equations method, we have performed numerical calculation for the various representations under the point group C_{4\nu} in order to determine at which temperature symmetry broken phases become more favorable than the symmetric phase. A surprisingly large number of phases has been observed. Some of them have an order parameter with many nodes in k-space. Commonly discussed types of order found by us are antiferromagnetism, d_{x^2-y^2}-wave singlet superconductivity, d-wave Pomeranchuk instability and flux phase. A few instabilities newly observed are a triplet analog of the flux phase, a particle-hole instability of p-type symmetry in the triplet channel which gives rise to a phase of magnetic currents, an s*-magnetic phase, a g-wave Pomeranchuk instability and the band splitting phase with p-wave character. Other weaker instabilities are found also. A comparison with experiments is made.Comment: revised version according to the referee remark

Ground state ferromagnetism in a doubly orbitally degenerate model

In the present paper the ground state of a double orbitally degenerate model at weak intra-atomic interaction is studied using the Green functions method. Beside the diagonal matrix elements of electron-electron interactions the model includes correlated hopping integrals and inter-atomic exchange interaction. The influence of orbital degeneracy with Hund's rule coupling, correlated hopping and inter-atomic direct exchange on the ferromagnetic ordering is investigated. The expressions for ground state energy and magnetization, the criterion of transition from paramagnetic to ferromagnetic ground state as functions of the model parameters are obtained. The obtained results are compared with some experimental data for magnetic materials.Comment: 13 pages, 11 eps figure

Temperature-induced metal-insulator transition in a non-symmetric Hubbard model at half-filling

In the present paper metal-to-insulator transition with the increase of temperature is studied in a narrow-band model with non-equivalent Hubbard subbands at half-filling. It is shown that the results obtained in the considered model are essentially distinct from those obtained in the Hubbard model. The results are applied to the interpretation of some experimental data.У цій роботі вивчається температурно-індукований перехід метал-діелектрик у вузькозонній моделі з нееквівалентними габбардівськими підзонами при половинному заповненні. Показано, що результати, отримані у розглядуваній моделі, суттєво відрізняються від результатів моделі Габбарда

Pressure-temperature phase diagram of the generalized Hubbard model with correlated hopping at half-filling

In the present paper, the pressure-temperature phase diagram of a generalized Hubbard model with correlated hopping in a paramagnetic state at half-filling is determined by means of a generalized mean-field approximation in the Green function technique. The constructed phase diagram describes the metal-to-insulator transition with increasing temperature, and the insulator-to-metal transition under the action of external pressure. The phase diagram can explain the paramagnetic region of the phase diagrams of some transition metal compoundsРобота присвячена побудові фазової діаграми тиск-температура узагальненої моделі Габбарда з корельованим переносом у парамагнітному стані при половинному заповненні зони з використанням узагальненого наближення Гартрі-Фока в методі функцій Ґріна. Побудована фазова діаграма описує перехід з металічного стану в діелектричний при збільшенні температури і перехід з діелектричного стану в металічний під дією зовнішнього тиску. Фазова діаграма може пояснити парамагнітні області фазових діаграм деяких сполук перехідних металів

Some Low-Temperature Properties of a Generalized Hubbard Model with Correlated Hopping

In the present paper we study some correlation effects in a generalized Hubbard model with correlated hopping within low-temperature region using a generalized mean-field approximation. It is shown that in a series of cases the model leads to consequences deviating essentially from those of the Hubbard model. We consider the possibility of applying the result to interpret the peculiarities of physical properties of systems with narrow energy bands.Comment: 2 pages, LaTex2e using Elsevier style, presented at LT22 Conference, Helsinki, August 199

Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections

The conductivity of the two-dimensional Hubbard model is particularly relevant for high-temperature superconductors. Vertex corrections are expected to be important because of strongly momentum dependent self-energies. We use the Two-Particle Self-Consistent approach that satisfies crucial constraints such as the Mermin-Wagner theorem, the Pauli principle and sum rules in order to reach non-perturbative regimes. This approach is reliable from weak to intermediate coupling. A functional derivative approach ensures that vertex corrections are included in a way that satisfies the f sum-rule. The two types of vertex corrections that we find are the antiferromagnetic analogs of the Maki-Thompson and Aslamasov-Larkin contributions of superconducting fluctuations to the conductivity but, contrary to the latter, they include non-perturbative effects. The resulting analytical expressions must be evaluated numerically. The calculations are impossible unless a number of advanced numerical algorithms are used. A maximum entropy approach is specially developed for analytical continuation of our results. The numerical results are for nearest neighbor hoppings. In the pseudogap regime induced by two-dimensional antiferromagnetic fluctuations, the effect of vertex corrections is dramatic. Without vertex corrections the resistivity increases as we enter the pseudogap regime. Adding vertex corrections leads to a drop in resistivity, as observed in some high temperature superconductors. At high temperature, the resistivity saturates at the Ioffe-Regel limit. At the quantum critical point and beyond, the resistivity displays both linear and quadratic temperature dependence and there is a correlation between the linear term and the superconducting transition temperature. A hump is observed in the mid-infrared range of the optical conductivity in the presence of antiferromagnetic fluctuations.Comment: 40 pages, 5 figures Published version. Main modifications with respect to v1: physical discusion of diagrams in figure 1 added at the end of section II D and discussion about the vanishing of the AL term at zero Matsubara frequency added at the end of appendix