One-dimensional (t,U,X) model: Ground-state phase diagram in a mean-field-type approximation

Ground-state instabilities in the one-dimensional Penson-Kolb-Hubbard model

“…Our mean-field-type approximation predicts results consistent with other works done at half filling. In the particular case of the PK model (U = 0) we have found for |W |/t < π/ sin k F a phase diagram similar to that corresponding to the Hubbard model in the same approximation [9]; at half filling, the only transition which occurs is a SDW − CDW at W = 0. However, beyond the limits |W |/t = π/ sin k F indicated by our approach, we expect a qualitative change in the ground-state of the PK model.…”

“…The correspondence between these quantities and the components of the vertex function can be found in Refs. [9]. The generalized susceptibilities are two-particle Green functions and they obey the Bethe-Salpeter equation.…”

“…(1) and arbitrary density; however, our results for the ground-state phase diagram are valid in a definite range of parameters determined below. We investigate the possible occurence of instabilities in the ground-state of the PKH model in the same manner [9] as it was done for the 1D (t, U, X) model [10] : within the (zero-temperature) Green-function formalism in the Bloch representation, the instabilities are signaled by the poles of the vertex function Γ which obeys the Bethe-Salpeter equation. We solve this equation in the approximation when the irreducible vertex part is just the bare potential and the single-particle propagator has the 'free' expression.…”

Pair Correlation Functions in One-Dimensional Correlated-Hopping Models

“…Pair correlations are strongest in both models for ∆t ≈ 1. For ∆t 1.5, there is a change in the ground-state properties of the Hirsch model, and superconducting correlations are strongly suppressed for large ∆t, which is in accordance with mean field results [9]. In the Bariev model, there is no such evident change.…”

“…The main interest is the question whether and how collective behaviour can lead to a compensation of the Coulomb repulsion between the electrons. As a possible explanation, models with correlated-hopping interactions are a subject of current research [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”