Model wave functions constructed from (1+1)D conformal field theory (CFT) have played a vital role in studying chiral topologically ordered systems. There usually exist multiple degenerate ground states when such states are placed on the torus. The common practice for dealing with this degeneracy within the CFT framework is to take a full correlator on the torus, which includes both holomorphic and antiholomorphic sectors, and decompose it into several conformal blocks. In this paper, we propose a pure chiral approach for the torus wave function construction. By utilizing the operator formalism, the wave functions are written as chiral correlators of holormorphic fields restricted to each individual topological sector. This method is not only conceptually much simpler, but also automatically provides us the anyon eigenbasis of the degenerate ground states (also known as the "minimally entangled states"). As concrete examples, we construct the full set of degenerate ground states for SO($n$)$_1$ and SU($n$)$_1$ chiral spin liquids on the torus, the former of which provide a complete wave function realization of Kitaev's sixteenfold way of anyon theories. We further characterize their topological orders by analytically computing the associated modular $S$ and $T$ matrices.
Translation invariance, topology, and protection of criticality in chains of interacting anyons
利用有限尺寸标度变元，可以从有限系统的低能谱中提取相互作用任意子链的临界性质。In Phys. Rev. Lett. 98，160409（2007），Feiguin等人表明，环面上的Fibonacci任意子的反铁磁（AFM）链与三临界伊辛模型处于相同的普适类，并且临界性受到拓扑对称性的保护。在本文中，我们首先回顾了图形形式主义的研究的任意子的光盘，并展示了如何这种形式主义可能会一直延伸到研究系统的表面上的更高的属。然后，我们采用这种图形形式主义研究有限环的相互作用的任意子在光盘和环面，并表明，分析光盘上必然产生的能量谱，这是一个子集，这是获得的环面。对于临界哈密顿量，可以从这个子集中提取出与系统的拓扑对称性有关的局部标度算子的标度维数。相关的考虑也适用于开链。
Universal Gates from Braiding and Fusing Anyons on Quantum Hardware
Harvard University（哈佛大学）；Quantinuum；Stony Brook University（石溪大学）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学杨振宁理论物理研究所）；University of Chicago（芝加哥大学）
Characterizing topological order by studying the ground states of an infinite cylinder
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。
Transparent Domain Walls through Information Convex Sets
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Sungkyunkwan University（成均馆大学）；Pennsylvania State University（宾夕法尼亚州立大学）；Beijing Institute of Mathematical Sciences and Applications（北京数学与应用科学研究所）；Korea Institute for Advanced Study（韩国高等科学研究院）
