EXACT GROUND-STATE CORRELATION-FUNCTIONS OF ONE-DIMENSIONAL STRONGLY CORRELATED ELECTRON MODELS WITH RESONATING-VALENCE-BOND GROUND-STATE

We investigate one-dimensional strongly correlated electron models whi ch have the resonating-valence-bond state as the exact ground state. T he correlation functions are evaluated exactly using the transfer matr ix method for the geometric representations of the valence-bond states . In this method, we only treat matrices with small dimensions. This e nables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insula ting. Since the corresponding noninteracting systems may be insulating or metallic, we can say that the gap originates from strong correlati on. The persistent currents of the present models are also investigate d and found to be exactly vanishing.