Site dilution in the half-filled one-band Hubbard model: Ring exchange, charge fluctuations, and application to La2Cu1-x(Mg/Zn)xO4

We study the ground-state quantum spin fluctuations around the Néel ordered state for the one-band (t,U) Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian H_s⁽⁴⁾ is generated using the canonical transformation method, expanding to order t(t/U)³ . H_s⁽⁴⁾ contains four-spin ring exchange terms as well as second- and third-neighbor bilinear spin-spin interactions. Transverse spin fluctuations are calculated to order 1/S using a numerical real-space algorithm first introduced by Walker and Walstedt [Phys. Rev. B 22, 3816 (1980)]. Additional quantum charge fluctuations appear to this order in t/U , coming from electronic hopping and virtual excitations to doubly occupied sites. The ground-state staggered magnetization on the percolating cluster decreases with site dilution x , vanishing very close to the percolation threshold. We compare our results in the Heisenberg limit, t/U→0 , with quantum Monte Carlo (QMC) results on the same model and confirm the existence of a systematic x -dependent difference between 1/S and QMC results away from x=0 . For finite t/U , we show that the effects of both the ring exchange and charge fluctuations die away rapidly with increasing t/U . We use our finite t/U results to make a comparison with results from experiments on La₂Cu_1-x(Mg/Zn)_xO₄ .