Short-range correlated eigenstates in the many-electron problem

Abstract

A general hamiltonian H of electrons in finite concentration, interacting via any two-body coupling inside a crystal of arbitrary dimension, is considered. The electron motion is described in the Hilbert space S φ , spanned by a basis of Slater determinants of one-electron Bloch wave functions. The diagonal part of H in the Slater determinant basis is called H D. Electron pairs of total momentum K and projected spin ξ = 0, ±1 are considered in this work. The Schrödinger equation ( H − ϵ) ψ = 0 is shown to include a class of solutions ψ, ϵ such that ( H D − ϵ) ψ = 0. It is also shown that this class of eigenvectors cannot sustain any kind of long-range order and that the associated two-body correlation functions, accordingly, decay as power laws.