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

TL;DR

This paper introduces the sea-boson method for studying various quantum many-body systems, demonstrating its effectiveness in analyzing Luttinger liquids, Wigner crystals, and higher-dimensional Fermi liquids, with exact solutions and new insights.

Contribution

It develops and applies the sea-boson approach to solve models of Luttinger liquids, Wigner crystals, and higher-dimensional Fermi liquids, providing new analytical tools and results.

Findings

Sea-boson method successfully solves Luttinger and Calogero-Sutherland models.

The anomalous exponent matches previous results by Mattis and Lieb.

The two-dimensional model exhibits Landau Fermi liquid behavior.

Abstract

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.