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

We study the ground state quantum spin fluctuations around the N'eel ordered state for the one-band ($t,U$) Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian, $H_{\mathrm{s}}^{(4)}$, is generated using the canonical transformation method, expanding to order $t(t\mathrm{/}U{)}^3$. $H_{\rm s}^{(4)}$ contains four-spin ring exchange terms as well as second and third neighbor bilinear spin-spin interactions. Transverse spin fluctuations are calculated to order $1\mathrm{/}S$ using a numerical real space algorithm first introduced by Walker and Walsteadt. Additional quantum charge fluctuations appear to this order in $t\mathrm{/}U$, 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, $t\mathrm{/}U\to 0$, with quantum Monte Carlo (QMC) results on the same model and confirm the existence of a systematic $x$-dependent difference between $1\mathrm{/}S$ and QMC results away from $x=0$. For finite $t\mathrm{/}U$, we show that the effects of both the ring exchange and charge fluctuations die away rapidly with increasing $t\mathrm{/}U$. We use our finite $t\mathrm{/}U$ results to make a comparison with results from experiments on La${}_2$Cu${}_{1-x}$(Mg/Zn)${}_x$O${}_4$.