Absence of highest-spin ground states in the Hubbard model

The Hubbard modelH=–tc_xc_y +U n_xn_x withN electrons and periodic boundary condition is studied onv-dimensionalL₁ × ... ×L_v lattices. It is shown that for any value ofU there is no ground state with maximal spin (S=N/2) in the following cases: (i) ^v (v2) at low electron densities; with one hole ift>0 andL_i is odd for somei; with two holes ift<0, or ift>0 and all theL_i are even. (ii) Thebcc lattice at low densities; with two holes ift<0, or ift>0 and all theL_i are even; with 2, ..., 6 holes ifL_i=L andt<0, or ift>0 andL is even. (iii) The triangular lattice at densities near 0 and 1 ift>0; with two holes ift<0; with 2, 3, 4 holes ift<0 andL₁=L₂. (iv) Thefcc lattice at densities near 0 and 1 ift>0; with two holes ift<0. Some results for the one dimensional model are also presented.