STAGGERED FLUX PHASE AND D-WAVE PHASE OF THE T-J MODEL

We have numerically evaluated the energy of the staggered flux phase state (SFP), the d-wave resonating valence bond state, and the mixed SFP and d-wave state (SFP + d) of the extended t-J model at various hole densities (delta). The flux per plaquette and the size of the d-wave gap are taken as variational parameters. The calculation includes the kinetic energy, spin energy, the effective hole-hole interaction and the three-site pair-hopping term. We found that the SFP is stable against the projected Fermi liquid up to delta congruent-to 20%. For moderately large J,J/t greater-than-or-equal-to 0.4, the SFP + d state may be favoured against the pure d-wave state but only at very low hole density (delta approximately 2%). These calculations show that the pure SFP state is never the ground state at hole densities of experimental interest.