VARIATIONAL DESCRIPTION OF A QUASI-HOLE EXCITATION IN A QUANTUM ANTIFERROMAGNET

An accurate variational ansatz is proposed for a single quasihole excitation in a two-dimensional quantum antiferromagnet. The trial state includes spin-hole and spin-hole-spin correlations, in addition to background antiferromagnetic spin-spin correlations. Background spin-spin correlations are induced by the Heisenberg antiferromagnetic exchange interaction and describe the zero-point motion of spin waves around the Neel state. Spin-hole and spin-hole-spin correlations describe "strings" of spins displaced by one lattice site along the hole path. This is a generalization of the Brinkman-Rice approach to include quantum spin fluctuations. We have used the Monte Carlo method to compute the variational energy and the spectral weight of the quasihole state in the t-J model on the square lattice, with the proposed ansatz. Comparison with exact results for the 4 x 4 lattice shows very good agreement for both energy and spectral weight, at k = (pi/2, pi/2) in the range 0 less-than-or-equal-to t/J less-than-or-equal-to 5. We report results for lattices of several sizes up to 16 x 16 in the above range of t/J and for the two values of k where the hole energy band attains its minimum [k = (pi/2, pi/2)] and maximum [k = (0,0)].