A Majorana fermion t-J model in one dimension

We study a rotation-invariant Majorana fermion model in one dimension using diagrammatic perturbation theory and numerical diagonalization of small systems. The model is inspired by a Majorana representation of the antiferromagnetic spin-1/2 chain, and it is similar in form to the t-J model of electrons, except that the Majorana fermions carry spin 1 and Z(2) charge. We discuss the implications of our results for the low-energy excitations of the spin-1/2 chain. We also discuss a generalization of our model from three species of Majorana fermions to N species; the SO(4) symmetric model is particularly interesting