三维晶格中的$p$轨道;费米子、玻色子和（奇异的）磁性模型
$p$ orbitals in 3D lattices; fermions, bosons and (exotic) models of magnetism
摘要：
我们演示了如何不同类型的$SU(3)$海森堡模型可以实现与使用的$p$轨道的三维光晶格。通过考虑一个莫特绝缘体与单位填充，动力学是很好地描述了一个有效的模型，来自微扰处理的隧道元素相对于现场的相互作用条款。这就产生了具有自由度的系统，它们是$SU(3)$群的生成元，这扩展了经常用于分析量子磁性的海森堡模型。由于玻色子和费米子情况下相互作用的不同性质，原子的选择决定了相应的有效哈密顿量的耦合将出现什么类型的各向异性。这些系统的检测和操作的实验方案，并讨论了选定的例子的基态的属性。
英文摘要：
We demonstrate how different types of $SU(3)$ Heisenberg models can be implemented with the use of the $p$ orbitals of three dimensional optical lattices. By considering a Mott insulator with unit filling, the dynamics is well described by an effective model derived from the perturbative treatment of the tunneling elements relative to the onsite interaction terms. This yields systems with degrees of freedom that are generators of the $SU(3)$ group, which extends the Heisenberg models frequently used to analyze quantum magnetism. Due to the different character of interactions in the bosonic and fermionic cases, the choice of atom determines what type of anisotropies will appear in the couplings of the corresponding effective Hamiltonians. Experimental schemes for detection and manipulation of these systems are presented, and properties of the ground states of selected examples are discussed.
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