Bosonization. Luttinger Liquid

Abstract

In this section we are going to focus our attention on the line of critical points g _1⊥ = 0 in the upper half-plane of Fig. 3.10. These are worth of study since, as stated in the previous chapter, the properties of the theory on that line give the low-energy physics on the whole region g _1‖ ≥ |g _1⊥|, where the backscattering is an irrelevant perturbation. The model with g _1⊥ = 0 is called the Tomonaga model[1]. A further simplification is achieved if one introduces an infinite linear dispersion relation for both left and right channels, as shown in Fig. 4.1. It is argued that the influence of the deeper, spurious electronic states can be neglected if one only cares about low-energy processes. The consequences of this variant are important since the model with the infinite linear dispersion relation and the interactions given in Figs. 3.2 and 3.3 is exactly solvable. This is called the Luttinger model[2]. Quite remarkably, this is a quantum field theory in which the complete summation of diagrams in perturbation theory can be achieved[3]. This can be done using the great degree of symmetry of the model: the dynamics conserves the number of particles of given spin in a given channel.