  Motivated by the problem of N coupled Hubbard chains, we investigate a
generalisation of the Schulz-Shastry model containing two species of
one-dimensional fermions interacting via a gauge field that depends on the
positions of all the particles of the other species. The exact many body ground
state of the model can be easily obtained through a unitary transformation of
the model. The correlation functions are Luttinger-like - i.e., they decay
through power laws with non-integer exponents. Through the interaction
dependent correlation functions of the two-particle operators, we identify the
relevant perturbations and hence, possible instabilities.
