用无限长圆柱的基态刻画拓扑序
Characterizing topological order by studying the ground states of an infinite cylinder
摘要：
给定一个拓扑有序相的微观晶格哈密顿量，我们描述了一个张量网络的方法来表征其紧急任意子模型，在手征相，也是它的无隙边理论。首先，通过数值优化获得无限长、有限宽圆柱体上完整的规范正交基态集的张量网络表示。这些基态中的每一个都被认为有不同的任意子通量穿过圆柱体。在手征相位中，每个基态的纠缠谱被认为揭示了相应的无隙边缘理论的不同扇区。然后通过截断并重新连接圆柱上的张量网络表示来产生环面上的准正交基。详细阐述了[Y. Zhang et al.Phys.Rev.B85，235151（2012）]，环面上的旋转产生基态的替代基，并且通过计算基之间的重叠，提取模矩阵S和U（包含不同任意子种类的互统计和自统计）。作为应用，我们利用二维密度矩阵重整化群研究了硬核玻色子Haldron模型。对这个晶格模型的普适性质的彻底表征，无论是在体还是在边缘，都明确地表明它的基空间实现了ν=1/2玻色子劳克林态。
英文摘要：
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network representation of a complete, orthonormal set of ground states on a cylinder of infinite length and finite width is obtained through numerical optimization. Each of these ground states is argued to have a different anyonic flux threading through the cylinder. In a chiral phase, the entanglement spectrum of each ground state is seen to reveal a different sector of the corresponding gapless edge theory. A quasi-orthogonal basis on the torus is then produced by chopping off and reconnecting the tensor network representation on the cylinder. Elaborating on the recent proposal of [Y. Zhang et al. Phys. Rev. B 85, 235151 (2012)], a rotation on the torus yields an alternative basis of ground states and, through the computation of overlaps between bases, the modular matrices S and U (containing the mutual and self statistics of the different anyon species) are extracted. As an application, we study the hard-core boson Haldane model by using the two-dimensional density matrix renormalization group. A thorough characterization of the universal properties of this lattice model, both in the bulk and at the edge, unambiguously shows that its ground space realizes the ν=1/2 bosonic Laughlin state.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
