Chiral phase states of the Hubbard Hamiltonian

We present a variational approach different from that based on Gutzwiller’s ansatz by investigating chiral flux-phase states of the Hubbard Hamiltonian in analogy to the treatment of the fractional quantum Hall effect. The proposed class of generalized Laughlin trial functions is specialized to permit detailed consideration of a set of states that includes a ferromagnetic ground state generated by a spontaneous gauge field in conjunction with a fictitious magnetic field having a flux commensurate with the filling. We evaluate the trial energy expectation values and demonstrate that the treatment is, at least, appropriate for the Hubbard model with sufficiently large on-site Coulomb repulsion and low electron densities. The members of the special set of trial states may be suitably classified by the flux quanta of the associated field and may be characterized either by integer or fractional quantum numbers. The excitations designated by fractional quantum numbers, which are not commensurate with the filling, are identified as flux-phase states breaking the symmetries of the lattice.