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We study the ground state quantum spin fluctuations around the N\'eel orderedstate for the one-band ($t,U$) Hubbard model on a site-diluted square lattice.An effective spin Hamiltonian, $H_{\rm s}^{(4)}$, is generated using thecanonical transformation method, expanding to order $t(t/U)^3$. $H_{\rms}^{(4)}$ contains four-spin ring exchange terms as well as second and thirdneighbor bilinear spin-spin interactions. Transverse spin fluctuations arecalculated to order $1/S$ using a numerical real space algorithm firstintroduced by Walker and Walsteadt. Additional quantum charge fluctuationsappear to this order in $t/U$, coming from electronic hopping and virtualexcitations to doubly occupied sites. The ground state staggered magnetizationon the percolating cluster decreases with site dilution $x$, vanishing veryclose to the percolation threshold. We compare our results in the Heisenberglimit, $t/U \to 0$, with quantum Monte Carlo (QMC) results on the same modeland 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 theeffects of both the ring exchange and charge fluctuations die away rapidly withincreasing $t/U$. We use our finite $t/U$ results to make a comparison withresults from experiments on La$_2$Cu$_{1-x}$(Mg/Zn)$_x$O$_4$.

Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4