GROUND-STATE OF THE 2-DIMENSIONAL ANTIFERROMAGNETIC HEISENBERG-MODEL STUDIED USING AN EXTENDED WIGNER-JORDON TRANSFORMATION

A two-dimensional (2D) Wigner-Jordon transformation which maps spin variables into spinless fermion variables is found and used to study the 2D spin-1/2 antiferromagnetic Heisenberg model. The transformation generates a fictitious gauge field in the XY component of the Heisenberg model, and hence induces an in-phase orbital current in the Ising component flowing around each elementary plaquette of the underlying lattice. The ground state of the Heisenberg model in a 2D square lattice is found to be an in-phase Neel flux phase, i.e., a coexisting state of the flux phase with in-phase orbital currents and a long-range antiferromagnetic spin order. The zero-temperature mean-field energy of the in-phase Neel flux state, E0 = -0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.