In these notes we review some of the basic features of the 2D Hubbard model, thought of as the appropriate model for the description of the Cu - O planes in the cuprate superconductors. We discuss briefly the weak-coupling regime of the model and, in the opposite limit, the mapping of the one band Hubbard model onto an AFM Heisenberg model at half filling and onto the t - J model below half filling. We discuss next Emery's three band model and its mapping onto the so-called "spin-fermion" model. Its continuum limit is discussed by making use of an adiabatic followed by a gradient expansion. We review briefly how the model maps onto a nonlinear sigma model and some of the features of the latter.

An introduction to the Hubbard model

PIERI, Pierbiagio
1997-01-01

Abstract

In these notes we review some of the basic features of the 2D Hubbard model, thought of as the appropriate model for the description of the Cu - O planes in the cuprate superconductors. We discuss briefly the weak-coupling regime of the model and, in the opposite limit, the mapping of the one band Hubbard model onto an AFM Heisenberg model at half filling and onto the t - J model below half filling. We discuss next Emery's three band model and its mapping onto the so-called "spin-fermion" model. Its continuum limit is discussed by making use of an adiabatic followed by a gradient expansion. We review briefly how the model maps onto a nonlinear sigma model and some of the features of the latter.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/245134
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