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 method. Simulations are performed on LxL 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 infinite 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 infinite 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