THEOREM ON THE ONE-DIMENSIONAL INTERACTING-ELECTRON SYSTEM ON A LATTICE

A theorem about the spin properties of the ground state and the ordering of the energy levels for different spins of an interacting-electron model including an arbitrary diagonal interacting potential, an antiferromagnetic exchange, and an electron pair-hopping term for particles on a one-dimensional lattice is stated and proved. We show that when the number of electrons N = 4n + 2 (n an integer) with periodic boundary conditions or N = 4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet. This theorem generalizes a similar theorem Lieb and Mattis proved for the one-dimensional interacting electron system.