Phenomenological Theory Of Marginal Fermi Liquid (mfl) Study

In 1989. Varma and collaborators have put forrward a phenomenological theory of Marginal Feimi Liquid (MFL). They have proven that the universal anomalies in the normal state of Cu-O high-temperature superconductors follow from a single hypothesis: There exist charge- and spin- density excitations with the absorptive part of the polarizability at low frequencies ω proportional to ω/T, where T is the temperature,and constant otherwise. The consequences of this hypothesis are worked out for a variety of physical properties including superconductivity.Following from the linear response theory, the dielectic function, then the density polarizability can be obtained from the retarded density correlation function DR.Thus, as soon as DR is given, the density polarizability P can be worked out.The main purpose of this article is to justify the hypothesis above. In this article the one-band Hubbard Model has been studied. A extensive Wick's theorem for the operator set {p k(?),σ k(?)} has been established. The temperature Green's function of density correlatio(?) has been culculated and then been extended analytically to the retarded density correlation function DR,then the imaginary part of the density polarrizability ImP I is obtained.It is found by numerical imitation that for a strongly correlated system with high doping (U~8t, δ~0.2). as a smooth function of q which is nonzero overr a substantial part of the Brillouin zone, ImP is proportional to ω/T at low frequencies (ω