Commensurate-flux-phase state of the t-J model

We propose a variational approach for the study of chiral flux-phase states. We present a class of variational wave functions of the generalized Laughlin-type. The generalization consists of the introduction of Gutzwiller projections and of a fictitious magnetic field. We classify antiferromagnetic chiral flux-phase states and evaluate analytically the corresponding expectation values of the t-J Hamiltonian at any value of filling. There are two types of chiral flux-phase states: commensurate and fractional. We have found that the minimal energy has a commensurate-flux-phase state for which the value of the flux of the orbital magnetic field equals the filling.