Influence of topological constraints and topological excitations: Decomposition formulas for calculating homotopy groups of symmetry-broken phases
Influence of topological constraints and topological excitations: Decomposition formulas for calculating homotopy groups of symmetry-broken phases
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拓扑约束和拓扑激励的影响：计算对称破缺相同伦群的分解公式
DOI：
10.1103/physrevb.95.134520
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Sho Higashikawa and Masahito Ueda
中科院分区：
文献类型：
--
作者：
樋口匠;真砂全宏;山中隆義;石田憲二;常盤欣文;H. S. Jeevan;C. Geibel;小和一弘,木村剛，若林裕助;Sho Higashikawa and Masahito Ueda
具有内自由度的系统的对称破缺相往往具有复杂的序参量，它产生了丰富的拓扑激励，并对它们的相互作用（拓扑影响）施加了拓扑约束，然而序参量的复杂性使得系统地处理拓扑激励和拓扑影响变得困难。为了克服这个问题，我们发展了一种计算同伦群的一般方法，并导出了用系统的阶数和状态的剩余阶数表示序参数流形的同伦群的分解公式。通过将这些公式应用于一般的单极子和三维Skyrmions，我们证明了它们的纹理是通过将相应的子代数替换为自旋而得到的。我们还证明了的离散对称性是拓扑影响存在的必要条件，并发现了拓扑影响对SU（3）-Heisenberg模型基态中由三个元素组成的非阿贝尔置换群所表征的skyrmion的影响.
A symmetry broken phase of a system with internal degrees of freedom often features a complex order parameter, which generates a rich variety of topological excitations and imposes topological constraints on their interaction (topological influence); yet the very complexity of the order parameter makes it difficult to treat topological excitations and topological influence systematically. To overcome this problem, we develop a general method to calculate homotopy groups and derive decomposition formulas which express homotopy groups of the order parameter manifoldin terms of those of the symmetryof a system and those of the remaining symmetryof the state. By applying these formulas to general monopoles and three-dimensional skyrmions, we show that their textures are obtained through substitution of the correspondingsubalgebra for thespin. We also show that a discrete symmetry ofis necessary for the presence of topological influence and find topological influence on a skyrmion characterized by a non-Abelian permutation group of three elements in the ground state of an SU(3)-Heisenberg model.