High-Tc superconductivity through a charge pairing mechanism in a strongly coupled disordered phase

We present a lattice field theory of spins coupled to Dirac fermions, as a model for the doped copper oxide compounds. Both the fermionic and spin degrees of freedom are treated dynamically. The influence of the charge carriers on the magnetic ordering follows automatically. The magnetic phase diagram at zero temperature is studied numerically and with Mean-Field methods. The Hybrid Monte Carlo algorithm is adapted to the O(3) non-linear sigma model constraint. The charged excitations in the various phases are studied at the Mean-Field level. Bound states of two charged fermions are found in a strongly coupled paramagnetic phase, without requiring a Fermi sea. We acquire a qualitative understanding of high-T$_c$ superconductivity through Bose-Einstein condensation of those dynamically bound pairs. The model also implies insulating behaviour at low doping, and Fermi liquid behaviour at large doping. We predict the possibility of reentrant superconductivity and the absence of superconductivity in spin-1 and spin-3/2 materials.