The singlet state in the Hubbard model with U

We discuss, in connection with the problem of the ground state in the Hubbard model with U=∞, the normal (nonmagnetic) N-state of a system over the entire range of electron concentrations n≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy e0(n) of the N-state is lower than the energy eFM(n) of a saturated ferromagnetic state for all values of n. Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N-state is stable for all values of n. A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T=0 acquires a Migdal discontinuity, whose magnitude depends on n. The energy of the N-state in this approximation is still lower than eFM(n) for n<1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n. Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state.