We construct a model for the value of the pair distribution function g↑↓(0) between antiparallel-spin electrons at contact in a two-dimensional electron gas with e2/r interactions, as a function of the coupling-strength parameter rs. The model involves an interpolation between the result of a low-rs expansion, including the second-order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. The interpolation formula is in excellent agreement with many-body calculations based on the ladder approximation. We further show through an STLS self-consistent calculation that g↑↓(0) is essentially independent of the state of spin polarization of the electron gas.

In the last years ample experimental evidence has shown that charge carriers in high-temperature superconductors are strongly correlated but also coupled with lattice vibrations (phonons), signaling that the true origin of high-Tc superconductivity can only be found in a proper combination of Coulomb and electron-phonon interactions. On this basis, we propose and study a model for high-Tc superconductivity, which accounts for realistic Coulomb repulsion, strong electron-phonon (Fröhlich) interaction and residual on-site (HubbardŨ ) correlations without any ad-hoc assumptions on their relative strength and interaction range. In the framework of this model, which exhibits a phase transition to a superconducting state with a critical temperature Tc well in excess of 100K, we emphasize the role ofŨ as the driving parameter for a BEC/BCS crossover. Our model lays a microscopic foundation for the polaron-bipolaron theory of superconductivity. We argue that the high-Tc phenomenon originates in competing Coulomb and Fröhlich interactions beyond the conventional BCS description.

We report analytical and numerical results on the two-particle states of the polaronic t-Jp model derived recently with realistic Coulomb and electron-phonon (Fröhlich) interactions in doped polar insulators. Eigenstates and eigenvalues are calculated for two different geometries. Our results show that the ground state is a bipolaronic singlet, made up of two polarons. The bipolaron size increases with increasing ratio of the polaron hopping integral t to the exchange interaction Jp but remains small compared to the system size in the whole range 0 ≤ t/Jp ≤ 1. Furthermore, the model exhibits a phase transition to a superconducting state with a critical temperature well in excess of 100K. In the range t/Jp ≤ 1, there are distinct charge and spin gaps opening in the density of states, specific heat, and magnetic susceptibility well above Tc.

In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green's functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J > 0) and anti-ferro (J < 0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.