Hole motion in a quantum Néel state

The spin-wave expansion is used to motivate a simple trial wave function for the N\'eel ground state of a spin-1/2 Heisenberg antiferromagnet on a square lattice; the wave function yields an upper bound on the ground-state energy per bond of (-0.3317±{}0.0002)J, where J is the exchange constant. The wave function is easily generalizable to the case where a single hole, with hopping matrix element t, is present. The hole energy-momentum relationship is determined for J/t>0.25; the minimum hole energy is always on the zone boundary at k=({π}/2,{π}/2). The hole bandwidth, W, has a maximum value of 1.24t at J=0.73t. The small parameter which makes all of these calculations possible is 1/(2Z-2), where Z=4 is the coordination number of the square lattice.