Variational description of a quasihole 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 Ne{}el state. Spin-hole and spin-hole 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×{}4 lattice shows very good agreement for both energy and spectral weight, at k=({π}/2,{π}/2) in the range 0{≤}t/J{≤}5. We report results for lattices of several sizes up to 16×{}16 in the above range of t/J and for the two values of k where the hole energy band attains its minimum [k=({π}/2,{π}/2)] and maximum [k=(0,0)].