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Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model

We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter $F_0^a$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism --- negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at $F_0^a=-1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange $J$ and Coulomb $V$ elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange $J<0$. Charge Landau parameter $F_0^s$ is lowered near half filling by increasing $U$ when the intersite Coulomb interaction $V$ is attractive, but in contrast to $F_0^a$ at $J<0$ it requires an attraction beyond a critical value $V_c$ to generate the divergence of the charge susceptibility at $F_0^s=-1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.