Staggered-flux normal state in the weakly doped t-J model

A normal (non-superconducting) ground state of the t-J model may be variationally approximated by a Gutzwiller-projected wave function. Within this approximation, at small hole doping near half-filling, the normal state favors staggered-flux ordering. Such a staggered-flux state may occur in vortex cores of underdoped high-temperature cuprate superconductors. From comparing the energies of the staggered-flux state and of the superconducting state, we numerically obtain the condensation energy. Extracting the superfluid density directly from the projected superconducting wave function, we can also estimate the coherence length at zero temperature.