QUANTUM DISORDERED PHASE IN A DOPED ANTIFERROMAGNET

A quantitative description of the transition to a quantum disordered p hase in a doped antiferromagnet, is obtained for the long-wavelength l imit of the spin-fermion model, which is given by the O(3) non-linear a model, a free fermionic part and current-current interactions. By ch oosing local spin quantization axes for the fermionic spinor we show t hat the low-energy limit of the model is equivalent to a U(1) gauge th eory, where both the bosonic and fermionic degrees of freedom are mini mally coupled to a vector gauge field. Within a large-N expansion, the strength of the gauge fields is found to be determined by the gap in the spin-wave spectrum, which is dynamically generated. The explicit d oping dependence of the spin-gap is determined as a function of the pa rameters of the original model. As a consequence of the above, the gau ge-fields mediate a long-range interaction among dopant holes and S-1/ 2 magnetic excitations only in the quantum disordered phase. The possi ble bound-states in this regime correspond to charge-spin separation a nd pairing.