Competition and possible coexistence of flux and resonating-valence-bond phases in the t -J model

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