ELEMENTARY EXCITATIONS IN ONE-DIMENSIONAL QUANTUM WIRES - EXACT EQUIVALENCE BETWEEN THE RANDOM-PHASE APPROXIMATION AND THE TOMONAGA-LUTTINGER MODEL

We show-contrary to the viewpoint that the random-phase approximation (RPA) is progressively worse in lower dimensions-that the simple random-phase approximation provides an exact description for intrasubband plasmon dispersion in one-dimensional quantum wires, by establishing a general equivalence between the RPA and the strongly correlated Tomonaga-Luttinger model for the elementary-excitation spectra in one-dimensional Fermi systems. We also discuss the formal analogy between intrasubband and intersubband collective modes in quantum wires by showing that the one dimensional intrasubband collective excitations can also be thought of as depolarization-shifted single-particle excitations. Our results explain why recent experimentally observed one-dimensional-plasmon dispersion in GaAs quantum wires can be quantitatively described by the RPA.