Off-diagonal long-range order in many-electron problem

The interacting electron Hamiltonian H = H-D + Sigma(K,zeta) H-K,H-zeta is considered in the Hilbert space spanned by Slater determinants of Bloch wave functions. HD consists of the diagonal part of H in this basis. K and zeta = 0, +/-1 stand for the total momentum and projected spin of electron pairs and H-K,H-zeta is the off-diagonal part of H describing the most general two-electron scattering process conserving K and zeta. It is shown that the eigenspectrum of H includes all eigenvalues of H-D+H-K,H-zeta for every K and zeta value. The associated eigenvectors of H are shown to have off-diagonal long-range order.