Abstract
Under a constraint of local self-energy, specific heat, the static magnetic susceptibility, and the compressibility for the one-band Hubbard model are calculated exactly in the framework of Fermi liquid theory. On the basis of the path integral formulation, exact relations among derivative self-energy and the vertex functions are derived, thereby establishing a general relation between the thermodynamic quantities. At half filling, as the charge Drude weight vanishes, both the magnetic susceptibility and specific heat are strongly enhanced, and the Wilson ratio saturates at 2, indicating that the local Fermi liquid behavior is stable against a ferromagnetic instability.
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