论文标题
无挫败的哈密顿量与图表上的拓扑顺序
Frustration-free Hamiltonian with Topological Order on Graphs
论文作者
论文摘要
人们普遍认为，在封闭的一维歧管上定义的模型不会产生拓扑顺序。在这里，我们构建了无挫败感的汉密尔顿人，在开放链{\ it和}多个基态退化（GSD）上具有对称性受保护的拓扑顺序（SPT），这与封闭链上的全球对称性无关。而不是全球对称性破坏，而是一个{\ it local}对称操作员，它与哈密顿式通勤并连接了多个接地状态，让人联想到各种绕组操作员如何连接福利型代码的拓扑上不同的接地状态。我们在开放链上求解的模型表明对称分数是SPT顺序的指示，在一般图上，GSD可以显示与第一个betti数字缩放 - 一种拓扑不变的，可计算该图的独立周期数量或一个维度孔的一个维孔。
It is commonly believed that models defined on a closed one-dimensional manifold cannot give rise to topological order. Here we construct frustration-free Hamiltonians which possess both symmetry protected topological order (SPT) on the open chain {\it and} multiple ground state degeneracy (GSD) that is unrelated to global symmetry breaking on the closed chain. Instead of global symmetry breaking, there exists a {\it local} symmetry operator that commutes with the Hamiltonian and connects the multiple ground states, reminiscent of how the topologically distinct ground states of the toric code are connected by various winding operators. Our model solved on an open chain demonstrates symmetry fractionalization as an indication of SPT order and on a general graph the GSD can be shown to scale with the first Betti number - a topological invariant that counts the number of independent cycles or one dimensional holes of the graph.
