Sea-boson theory of Landau-Fermi liquids, Luttinger liquids and Wigner crystals

摘要

It is shown how Luttinger liquids may be studied using sea-bosons. The main advantage of the sea-boson method is its ability to provide information about short-wavelength physics in addition to the asymptotics and is naturally generalizable to more than one dimension. In this article, we solve the Luttinger model and the Calogero-Sutherland model, the latter in the weak-coupling limit. The anomalous exponent we obtain in the former case is identical to the one obtained by Mattis and Lieb. We also apply this method to solve the two-dimensional analog of the Luttinger model and show that the system is a Landau-Fermi liquid. Then we solve the model of spinless fermions in one dimension with long-range (gauge) interactions and map the Wigner crystal phase of the system.