This article reviews theoretical and experimental developments for one-dimensional Fermi
gases. Specifically, the experimentally realized two-component delta-function interacting …

We review the progress in the theory of one-dimensional (ID) Fermi liquids which has
occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle …

A new approach to the single-band Hubbard model is described in the general context of
many-body theories. It is based on enforcing conservation laws, the Pauli principle and a …

We review fundamental issues arising in the exact solution of the one-dimensional Hubbard
model. We perform a careful analysis of the Lieb–Wu equations, paying particular attention …

We reconsider the spectrum of the Luttinger liquid (LL) usually understood in terms of
phonons (density fluctuations), and within the context of bosonization we give an alternative …

We review the theory of interacting Fermi systems whose low-energy physics is dominated
by forward scattering, that is scattering processes generated by effective interactions with …

The strong-coupling perturbation theory of the Hubbard model is presented and carried out
to order (t/U) 5 for the one-particle Green function in arbitrary dimension. The spectral weight …

A fermion-spin transformation is used to implement the charge-spin separation, and is
developed to study the low-dimensional tJ model. In this approach, the charge and spin …

The one dimensional tJ Hamiltonian is diagonalized exactly for the supersymmetric case
2t=±J using the Bethe ansatz. In this limit it is identical with models previously considered by …

The interplay between magnetism and doping is at the origin of exotic strongly correlated
electronic phases and can lead to novel forms of magnetic ordering. One example is the …