Tomonaga's theory for collective motion of fermions: Basic concept of one-dimensional correlated electrons

Abstract

In 1950, Tomonaga published a pioneering paper on collective motion of interacting fermions in one spatial dimension, which now establishes the basic concept of one-dimensional quantum critical phenomena, the so-called Tomonaga-Luttinger liquid. We briefly discuss fundamental properties of the Tomonaga-Luttinger liquid in comparison with the Fermi liquid. We then explain how (1+1) dimensional conformai field theory can be used to describe universal properties of the Luttinger liquid. Some examples of recent experimental observations are also addressed.