Chern Gia-Wei, Wu Congjun
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061127. doi: 10.1103/PhysRevE.84.061127. Epub 2011 Dec 15.
We demonstrate the existence of an orbital Coulomb phase as the exact ground state of a p-orbital exchange Hamiltonian on the diamond lattice. The Coulomb phase is an emergent state characterized by algebraic dipolar correlations and a gauge structure resulting from local constraints (ice rules) of the underlying lattice models. For most ice models on the pyrochlore lattice, these local constraints are a direct consequence of minimizing the energy of each individual tetrahedron. On the contrary, the orbital ice rules are emergent phenomena resulting from the quantum orbital dynamics. We show that the orbital ice model exhibits an emergent geometrical frustration by mapping the degenerate quantum orbital ground states to the spin-ice states obeying the 2-in-2-out constraints on the pyrochlore lattice. We also discuss possible realization of the orbital ice model in optical lattices with p-band fermionic cold atoms.
我们证明了轨道库仑相作为金刚石晶格上p轨道交换哈密顿量的精确基态的存在。库仑相是一种涌现态，其特征是代数偶极关联以及由底层晶格模型的局部约束（冰规则）产生的规范结构。对于大多数烧绿石晶格上的冰模型，这些局部约束是使每个四面体能量最小化的直接结果。相反，轨道冰规则是量子轨道动力学产生的涌现现象。我们通过将简并量子轨道基态映射到服从烧绿石晶格上2进2出约束的自旋冰态，表明轨道冰模型表现出涌现几何阻挫。我们还讨论了在具有p能带费米冷原子的光学晶格中实现轨道冰模型的可能性。
