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

References in corpus (7)

• Quantum magnetism and criticality
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model
• Thermodynamics of impurities in the anisotropic Heisenberg spin-1/2 chain
• Impurity-induced frustration in correlated oxides
• Magnetic excitations in SrCu2O3: a Raman scattering study
• Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets

Cited by in corpus (1)

• 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