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

Abstract

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, $H_{\mathrm{s}}^{(4)}$, is generated using the canonical transformation method, expanding to order $t(t/U{)}^3$. $H_{\mathrm{s}}^{(4)}$ 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 Walsteadt. 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, $t/U\to 0$, 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 La${}_2$Cu${}_{1-x}$(Mg/Zn)${}_x$O${}_4$.

21 pages, 2 columns. 13 figures

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Cited by in corpus (9)

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• Low energy theory of the t-t'-t''-U Hubbard Model at half-filling: interaction strengths in cuprate superconductors and an effective spin-only description of La_2CuO_4
• Antiferromagnetism of Zn${}_2$VO(PO${}_4{)}_2$ and the dilution with Ti${}^{4+}$
• Square-lattice magnetism of diaboleite Pb2Cu(OH)4Cl2
• Evidence for impurity-induced frustration in La2CuO4
• Antiferromagnetism beyond classical percolation threshold in the site-diluted half-filled one-band Hubbard model in three dimensions
• Impurity-induced frustration: low-energy model of diluted oxides
• High temperature non-collinear magnetism in a classical bilinear-biquadratic Heisenberg model
• Simulation of the Ring-exchange Models with Projected Entangled Pair States