ABSTRACT
This chapter presents the energy spectrum and the momentum distribution of the Frohlich–Toyozawa–Luttinger liquid. The one-dimensional many-electron problem has generated renewed interest after the discovery of quasi-one dimensional solids such as carbon nanotubes, quantum wires, and other one-dimensional systems. Tomonaga was the first to solve the one-dimensional interacting fermion problem exactly using bosonization and certain approximations regarding the commutator of the density operators. Marino considered a one-dimensional acoustic many-polaron Hamiltonian within the framework of the Luttinger model and showed that for a certain range of the coupling constants the system would exhibit a metallic behavior because the spectrum contains gapless collective excitations of polaronic plasmons. Rao et al. have exactly solved the one-dimensional interacting electron problem within the framework of Luttinger model incorporating both the electron-optical-phonon interaction and the electron-acoustic-phonon interaction along with the electron-electron interaction to obtain the energy spectrum.
