Two Theorems on Pseudo-spin in the Hubbard Model

An inequality of the eigenvalues of the reduced density matrix ${\rho }_2$ at finite temperature in the Hubbard model is obtained by means of the Bogolyubov inequality. The quasi-average of ${\tilde{S}}^{+}$ in a simple symmetry-breaking perturbation of the Hamiltonian for a bipartite lattice is shown to be zero.