On strongly correlated electrons in metals

Abstract

A procedure, dedicated to superconductivity, is extended to study the properties of interacting electrons in normal metals in the thermodynamic limit. Each independent-electron band is shown to split into two correlated -electron bands. Excellent agreement is achieved with Bethe's wave-function for the one-dimensional Hubbard model. The groundstate energy, reckoned for the two-dimensional Hubbard Hamiltonian, is found to be lower than values, obtained thanks to the numerical methods. This analysis applies for any spatial dimension and temperature.

Bethe’s Wave-Function Revisited

“…The x P coefficients will be assessed by analysing the two-body scattering, embodied by h 0 , h 1 . As a matter of fact, the latter turns out to be model dependent and to differ according to whether both electrons, partaking in the scattering process, have parallel or anti-parallel spin, which is referred to below as triplet or singlet case, respectively, for the sake of comparison with a previous work [7].…”

“…Furthermore it is in order to compare ε s with the electronic energy η 2 , obtained with help of the correlated Fermi gas (CFG) model [7] in normal metals, the characteristic features of which will be recalled now for self-containedness. Each independent-electron band of dispersion ϵ(k ∈ [−π, π]), as given in Eq.…”

“…Then the groundstate energy will be compared with data [6], obtained previously for the Hubbard Hamiltonian [3,4]. An additional comparison will be carried out with the data, resulting from the correlated Fermi gas model, introduced recently [7] to account for the properties of interacting electrons in normal metals. This method will be further applied to electrons interacting on neighbouring sites [8], which was believed so far to lie out of the scope of Bethe's wave-function [1][2][3][4].…”

Properties of Bound Electron Pairs

“…so that the outcome of two-electron scattering differs 21 according to whether the incoming electrons have same or opposite spin direction, although the Coulomb interaction is spinindependent.…”

“…, turns6 continuously into a MBE state Φ at finite concentration c s . As recalled above for a single pair, the corresponding Schrödinger equation (H 2 − N E) Φ = 0 be recast21 , but only for N → ∞, into…”