Large-Nlimit of the square-latticet-Jmodel at (1/4 and other filling fractions

We present a mean-field theory of the t-J model on a square lattice that becomes exact in a particular large-N limit. A detailed study of the free-energy manifold is carried out for the case of filling fraction {ν}=(1/4 as a function of t/J. Over the manifold examined, the ground state is either an insulating crystal of an N-hole bound state (for small t/J) or a normal Fermi liquid (for large t/J). For (1/4{≤}{ν}{≤} 1) / 2 , and t=0⁺, states with the localized holes, and nonzero spin correlations restricted to clusters of 4 or smaller, are global free-energy minima; in particular they are lower in energy than the state with uniform flux {Φ}={ν}, with staggered flux or a normal Fermi liquid.