Z3 topological order in the face-centered-cubic quantum plaquette model
Z3 topological order in the face-centered-cubic quantum plaquette model
复制标题
面心立方量子板模型中的 Z3 拓扑序
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Devakul
中科院分区：
文献类型：
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作者：
T. Devakul
我们研究了面心立方(FCC)晶格上硬核量子斑块模型(QPM)的共振单重态价斑(RSVP)相的拓扑有序。为此，我们构造了局域斑块共振的Rohksar-Kivelson型哈密顿量。我们通过确定一个$mathbb{Z}_3$拓扑常数(这导致了$3$环面上$3^3$倍的拓扑基态简并)和拓扑点状电荷和环状磁激发，证明了该模型具有$mathbb{Z}_3$拓扑序。我们还考虑了该模型的一个精确可解推广，它使得$mathbb{Z}_3$序的几何起源是明确的。对于其他模型和晶格，这样的推广产生了各种各样的拓扑相，其中一些是新的分数相。
We examine the topological order in the resonating singlet valence plaquette (RSVP) phase of the hard-core quantum plaquette model (QPM) on the face centered cubic (FCC) lattice. To do this, we construct a Rohksar-Kivelson type Hamiltonian of local plaquette resonances. This model is shown to exhibit a $mathbb{Z}_3$ topological order, which we show by identifying a $mathbb{Z}_3$ topological constant (which leads to a $3^3$-fold topological ground state degeneracy on the $3$-torus) and topological point-like charge and loop-like magnetic excitations which obey $mathbb{Z}_3$ statistics. We also consider an exactly solvable generalization of this model, which makes the geometrical origin of the $mathbb{Z}_3$ order explicitly clear. For other models and lattices, such generalizations produce a wide variety of topological phases, some of which are novel fracton phases.