半满单能带哈伯德模型中的格位稀释：环交换、电荷涨落及对La 2 Cu_{1-x}（Mg/Zn）_xO 4的应用
Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4
摘要：
本文研究了在格位稀释的正方晶格上，单带（$t,U$）哈伯德模型的Néel有序态周围的基态量子自旋涨落。利用正则变换方法生成了一个有效的自旋哈密顿量$H_{\rm s}^{(4)}$，展开到$t(t/U)^3$阶. $H_{\rm s}^{(4)}$包含四自旋环交换项以及第二和第三近邻双线性自旋-自旋相互作用。横向自旋起伏计算顺序$1/S$使用数值实空间算法首先介绍了沃克和Walsteadt。额外的量子电荷波动出现在$t/U$中的这个顺序，来自电子跳跃和虚激发双占据的网站。基态交错磁化的扩散团簇减少与现场稀释$x$，消失非常接近逾渗阈值。我们比较我们的结果在海森堡极限，$t/U \to 0$，量子蒙特卡罗（QMC）的结果在同一模型，并确认存在一个系统的$x$依赖的差异之间的$1/S$和QMC的结果远离$x=0$。对于有限的$t/U$，我们表明，环交换和电荷波动的影响消失迅速增加$t/U$。我们使用我们的有限$t/U$结果进行比较，从La $_2$ Cu $_{1-x}$（Mg/Zn）$_x$ O $_4$的实验结果。
英文摘要：
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, $H_{\rm s}^{(4)}$, is generated using the canonical transformation method, expanding to order $t(t/U)^3$. $H_{\rm s}^{(4)}$ contains four-spin ring exchange terms as well as second and third neighbor bilinear spin-spin interactions. Transverse spin fluctuations are calculated to order $1/S$ 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$_4$.
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