ABSENCE OF HIGHEST-SPIN GROUND-STATES IN THE HUBBARD-MODEL

The Hubbard model H = -t-SIGMA-c(x-sigma) dagger c(y-sigma) + U SIGMA-n(x) up n(x) down with N electrons and periodic boundary condition is studied on nu-dimensional L1 x ... x L-nu lattices. It is shown that for any value of U there is no ground state with maximal spin (S = N/2) in the following cases: (i) Z-nu (nu greater-than-or-equal-to 2) at low electron densities; with one hole if t > 0 and L(i) is odd for some i; with two holes if t < 0, or if t > 0 and all the L(i) are even. (ii) The bcc lattice at low densities; with two holes if t < 0, or if t > 0 and all the L(i) are even; with 2,...,6 holes if L(i) = L and t < 0, or if t > 0 and L is even. (iii) The triangular lattice at densities near 0 and 1 if t > 0; with two holes if t < 0; with 2, 3, 4 holes if t < 0 and L1 = L2. (iv) The fcc lattice at densities near 0 and 1 if t > 0; with two holes if t < 0. Some results for the one dimensional model are also presented.