Competition and possible coexistence of flux and resonating-valence-bond phases in thet-Jmodel

The competition and possible coexistence of the flux phase and pairing states are considered\udwithin the slave-boson approach. In addition to the gauge-field coupling holons and spinons, a\udstatistical gauge field is introduced to account for the hard-core nature of holons. Using the\udequivalence of z-uniform and -staggered fluxes, we show the possibility of reducing the staggered\udflux and guaranteeing the commensurability condition of the uniform flux for holons at the same\udtime. For certain dopings the frustration of the spinon gauge field to holon motion can be compensated\udby the holon's own statistical gauge field. Contrary to earlier conclusions of other authors,\udwe find that the flux phase can coexist with the resonating-valence-bond (RVB) states\udbelow a critical doping concentration &,beyond which the d-wave RVB state takes over