SHORT-RANGE CORRELATED EIGENSTATES IN THE MANY-ELECTRON PROBLEM

A general hamiltonian H of electrons in finite concentration, interact ing via any two-body coupling inside a crystal of arbitrary dimension, is considered. The electron motion is described in the Hilbert space S-phi, spanned by a basis of Slater determinants of one-electron Bloch wave functions. The diagonal part of H in the Slater determinant basi s is called H-D. Electron pairs of total momentum K and projected spin zeta = 0, +/-1 are considered in this work. The Schrodinger equation (H - epsilon)psi = 0 is shown to include a class of solutions psi, eps ilon such that (H-D - epsilon)psi = 0. It is also shown that this clas s of eigenvectors cannot sustain any kind of long-range order and that the associated two-body correlation functions, accordingly, decay as power laws.