Pair Correlation Functions in One-Dimensional Correlated-Hopping Models

Abstract

We investigate ground-state properties of two correlated-hopping electron models, the Hirsch and the Bariev model. Both models are of recent interest in the context of hole superconductivity. Applying the Lanczos technique to small clusters, we numerically determine the binding energy, the spin gaps, correlation functions, and other properties for various values of the bond-charge interaction parameter. Our results for small systems indicate that pairing is favoured in a certain parameter range. However, in contrast to the Bariev model, superconducting correlations are suppressed in the Hirsch model, for a bond-charge repulsion larger than a critical value.

Single-site entanglement at the superconductor-insulator transition in the Hirsch model

“…confirms that for x > x c , u < u c a new phase opens, characterized by negative E b . This fact could correspond simply to phase separation, as well as to superconductivity, both phenomena having been observed in previous numerical studies by varying x, u, and n. 8,10 In order to understand the nature of the new phase in our case, we have studied both singlet pair correlations η † i η j and the spin gap…”

“…Still, at x = 1 and for u ≤ u c (n), the system enters a phase characterized by off-diagonal long-range order (ODLRO 6 ) and nonvanishing pairing correlation, both features being an indication of possible superconducting order, which is absent at x = 1 due to the high degeneracy of the ground state (g.s.). The possible presence of superconducting order has been investigated also for x = 1 at various n. It turns out that this is the case, at least for low enough u and appropriate x and n values; 7,8,9 also, a spin gap opens for n > 1, 2,8 whereas, as for the transition to the insulating phase, results at x = 1 are far from exhaustive, 9,10 though supporting the possibility of a finite u c away from the weak-coupling limit.…”

Quantum Monte Carlo and exact diagonalization study of a dynamic Hubbard model

“…Note that for larger g the antiadiabatic limit is approached for larger ω 0 , in accordance with the discussion following Eq. (19).…”

“…a Hubbard model where the electronic hopping amplitude depends on the occupation of the two sites involved in the hopping process. This model is known to exhibit superconductivity when the Fermi level is close to the top of the band, both from mean field calculations [13][14][15], exact diagonalization [16][17][18], and other exact techniques [19,20]. Furthermore, a variety of observable properties have been calculated in this limit such as thermodynamics [13,21], tunneling [22], optical properties [23], pressure dependence [21], etc.…”

Why holes are not like electrons: A microscopic analysis of the differences between holes and electrons in condensed matter

“…This 'correlated hopping' Hamiltonian has been extensively studied in recent years by approximate and exact techniques, and the reader is referred to the references for detailed information [9,[23][24][25][26][27][28][29][30][31][32]. The condition for superconductivity in the limit of low hole concentration is [32] K > (1 + u)(1 + w) − 1 (62) with K = 2z∆t/D, u = U/D, w = zV /D, with z the number of nearest neighbors to a site and D the (renormalized) bandwidth.…”