Propagator-Renormalized Perturbation Theory for the Hubbard Model

Abstract

Anderson [1] has argued forcefully that the unusual properties of the high temperature super-conductors for T > T _c place these materials in the universality class described by Haldane’s Luttinger liquid theory (LL) [2] instead of the more familiar class of metals governed by Landau’s Fermi liquid theory. The proven examples of Luttinger liquids are all one dimensional systems where the breakdown of the Fermi liquid picture can be traced to susceptibilities which diverge for T → 0 on account of the 1D analog of perfect Fermi surface nesting. The low-energy elementary excitations of the LL ground state exhibit separation of spin and charge, and if one trys to cast the one-electron Green’s function into standard Fermi liquid form, the resulting quasiparticle renormalization factor a _k retains a strong frequency and temperature dependence, and vanishes as a power law when these variables tend to zero.