MOTT-HUBBARD METAL-INSULATOR-TRANSITION - A CHAIN-CLUSTER FERMI-LINEARIZED APPROACH TO THE 2-D HUBBARD SYSTEM

We define a chain-cluster Fermi-linearized Hubbard model, in which the hopping between adjacent 1-d chains is described in terms of an order parameter (valued in a suitable Grassmann field) describing the (transverse) intra-bond correlation, whereas the intra-chain hopping is treated rigorously. The free energy of the 2-d Hubbard model, where neighbouring chains are connected by hopping processes, can be straightforwardly reconducted to that—evaluated self-consistently—of the 1-d model. The self-consistency equations for the one-dimensional chain, when solved explicitly using the exact Lieb-Wu-Takahashi equations, lead to the appearance of a phase transition, for finite values of the Coulomb repulsion strength U (U>U c, where U c is a critical finite value of U), which can be interpreted as evidence for a mott-Hubbard-type metal-insulator transition.