One-Dimensional Fermions and Bosonization

Abstract

This chapter deals with interaction effects in one-dimensional (1D) fermions. Because of the restricted spatial motion, interaction effects are stronger than in higher dimensional systems. Detailed treatment is provided for a powerful method called bosonization, which regards density fluctuation of 1D fermions as a bosonic object. In terms of bosonization, it is possible to discuss such interesting states as non-Fermi liquid with power-law decay of correlation functions, and separation of spin and charge degrees of freedom, both caused by mutual interactions. A state with an energy gap only for the charge sector is called the Mott insulating state, while the energy gap only for the spin sector corresponds to superconductivity. Finally we revisit the Kondo state from the 1D point of view.