Exact Momentum Distribution of a Fermi Gas in One Dimension

Abstract

We introduce an exactly solvable model of a fermi gas in one dimension and compute the momentum distribution exactly. This is based on a generalisation of the ideas of bosonization in one dimension. It is shown that in the RPA limit(the ultra-high density limit) the answers we get are the exact answers for a homogeneous fermi gas interacting via a two-body repulsive coulomb interaction. Furthermore, the solution may be obtained exactly for arbitrary functional forms of the interaction, so long as it is purely repulsive. No linearization of the bare fermion dispersion is required. We find that for the interaction considered, the fermi surface is intact for weak repulsion and is destroyed only for sufficiently strong repulsion. Comparison with other models like the supersymmetric t-J model with inverse square interactions is made.