Phase-diagram and quasiparticles of a lattice SU(2) scalar-fermion model in (2+1) dimensions

The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in (2+1) dimensions is studied numerically and with Mean-Field methods. Special attention is devoted to the strong coupling regime. We have developed a new method to adaptate the Hybrid Monte Carlo algorithm to the O(3) non-linear $\sigma$ model constraint. The charged excitations in the various phases are studied at the Mean-Field lev el. Bound states of two charged fermions are found in a strongly coupled {\it paramagnetic} phase. On the other hand, in the strongly coupled antiferromagnetic phase fermionic excitations around momenta $(\pm\frac{\pi}{2},\pm\frac{\pi}{2},\pm\frac{\pi}{2})$ emerge.