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Sea-Boson Theory of Landau Fermi Liquids, Luttinger Liquids and Wigner Crystals

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 generalisable 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.

preprint2004arXivOpen access
Girish S. Setlur
cond-mat.str-el
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Girish S. Setlur

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