Haegeman J, Zauner V, Schuch N, Verstraete F
Department of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, B-9000 Ghent, Belgium.
Vienna Center for Quantum Technology, University of Vienna, Boltzmanngasse 5, 1090 Wien, Austria.
Nat Commun. 2015 Oct 6;6:8284. doi: 10.1038/ncomms9284.
The low-temperature dynamics of quantum systems are dominated by the low-energy eigenstates. For two-dimensional systems in particular, exotic phenomena such as topological order and anyon excitations can emerge. While a complete low-energy description of strongly correlated systems is hard to obtain, essential information about the elementary excitations is encoded in the eigenvalue structure of the quantum transfer matrix. Here we study the transfer matrix of topological quantum systems using the tensor network formalism and demonstrate that topological quantum order requires a particular type of 'symmetry breaking' for the fixed point subspace. We also relate physical anyon excitations to domain-wall excitations at the level of the transfer matrix. This formalism enables us to determine the structure of the topological sectors in two-dimensional gapped phases very efficiently, therefore opening novel avenues for studying fundamental questions related to anyon condensation and confinement.
量子系统的低温动力学由低能本征态主导。特别是对于二维系统，可能会出现诸如拓扑序和任意子激发等奇异现象。虽然很难获得强关联系统完整的低能描述，但关于基本激发的重要信息编码在量子转移矩阵的本征值结构中。在这里，我们使用张量网络形式研究拓扑量子系统的转移矩阵，并证明拓扑量子序对于定点子空间需要一种特殊类型的“对称性破缺”。我们还在转移矩阵层面将物理任意子激发与畴壁激发联系起来。这种形式使我们能够非常有效地确定二维能隙相中的拓扑扇区结构，从而为研究与任意子凝聚和禁闭相关的基本问题开辟了新途径。
