Quasihole excitation in a quantum antiferromagnet: Variational Monte Carlo calculation

We study a single quasihole excitation in a quantum antiferromagnet using a variational wave function that includes spin-spin as well as spin-hole correlations. The wave function can be cast in the form of a complex correlation operator acting on a Marshall-type wave function for the spin background. Such a correlation operator, featuring momentum-dependent spin-hole correlations, is shown to correspond to a coherent local rotation of the spins, which can be also interpreted as a ''spin-backflow'' current, analogous to the Feynman-Cohen backflow current in helium liquids. The variational Monte Carlo method is used to calculate the hole excitation spectrum on a square lattice for the t-J model with this wave function. Comparing our results with available exact results on a 4x4 square lattice, we find qualitative and semiquantitative agreement. We provide results obtained on much larger lattices. We find that the quasihole energy band attains its minimum at k=(±π/2,±π/2) while the hole mass is strongly anisotropic in different directions of k space. The quasihole excitation creates both a planar long-range distortion of the antiferromagnetic (AF) moment of the background δm†(r→∞)∼(k·r)/r2 and a ferromagnetic moment localized in the immediate neighborhood of the hole, pointing in the perpendicular direction. The magnitude of the ferromagnetic moment depends on the momentum of the excitation, and at the minimum of the hole band only the long-range AF planar distortion is present