Green's-function Monte Carlo study of the two-dimensional, spin-1/2 XY ferromagnet.

The ground states of quantum spin 1/2 XY ferromagnetic triangular and square systems are investigated with the Green's function Monte Carlo (GFMC) method. Simulations are performed on L L two-dimensional lattices with L up to 19. The long range orders as well as ground state energies are obtained for both lattices and are extrapolated to innnite system size. The long range order (LRO) is computed directly using kernels from the system Hamiltonian and a `perturbed' Hamiltonian involving the LRO operator. It is seen that LRO exists in the innnite triangular lattice, contrary to conclusions drawn from previous exact diagonalization studies. The second-order spin-wave theory again appears to yield very good results on these systems.