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

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

Signatures of Electronic Nematic Phase at Isotropic-Nematic Phase Transition

The electronic nematic phase occurs when the point-group symmetry of the lattice structure is broken, due to electron-electron interactions. We study a model for the nematic phase on a square lattice with emphasis on the phase transition between isotropic and nematic phases within mean field theory. We find the transition to be first order, with dramatic changes in the Fermi surface topology accompanying the transition. Furthermore, we study the conductivity tensor and Hall constant as probes of the nematic phase and its transition. The relevance of our findings to Hall resistivity experiments in the high-$T_c$ cuprates is discussed.Comment: 5 pages, 3 figure

Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory

This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments has been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the Two-Particle Self-Consistent Approach, Variational Cluster Perturbation Theory (or variational cluster approximation), and Cellular Dynamical Mean-Field Theory.Comment: 32 pages, 51 figures. Slight modifications to text, figures and references. A PDF file with higher-resolution figures is available at http://www.physique.usherbrooke.ca/senechal/LTP-toc.pd