发表机构
University of Illinois at Urbana-Champaign; Sungkyunkwan University; Pennsylvania State University; Beijing Institute of Mathematical Sciences and Applications; Korea Institute for Advanced Study（伊利诺伊大学厄巴纳-香槟分校; 成均馆大学; 宾夕法尼亚州立大学; 北京数学与应用科学研究所; 韩国高等科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出基于信息凸集的纠缠引导框架，直接从基态波函数提取透明畴壁信息，推导融合规则与量子维度，揭示其对称性，并应用于多个模型。
AI 中文摘要
在(2+1)维拓扑有序多体态中，透明（拓扑可变形）畴壁对局域拓扑探针不可见，但可改变基态简并度（GSD）并使穿过它们的任意子发生嬗变。在此，我们发展了一种基于纠缠引导的框架，利用局部和不可收缩环带上的信息凸集（ICSs），直接从环面上阿贝尔拓扑相固定点处的基态波函数中提取关于透明畴壁的信息，而无需将范畴缺陷数据作为输入。我们推导了控制任意子在不可收缩环带ICS极值点上作用的融合规则，并确定了它们的量子维度。在互补环周围传输下不变的极值点与最小熵态（MESs）一一对应，其数目等于GSD。最大拓扑纠缠熵（TEE），$γ_{\rm LW}^{\max}=\log({D}/d_α)$，探测穿过所选环带的畴壁净效应，其中${ D}$是总量子维度，$d_α$是其ICS极值点的量子维度。相比之下，最大纠缠不对称性是$ΔS_X^{\max}=\log\mathrm{GSD}$。该值对两个环带方向相同，并反映了透明畴壁的综合效应。我们进一步证明，透明畴壁可以产生同时支撑在两个选定基本环上的对称性，这些对称性不能分解为两个1-形式对称算符的乘积，每个算符支撑在一个环上。通过将它们对MESs的作用与任意子隧穿和融合规则联系起来，我们阐明了这些对称性如何连接不同的基态。此外，我们将该框架应用于Wen的平板模型、各向异性偶极环面码和秩-2环面码。
英文摘要
In $(2+1)$-dimensional topologically ordered many-body states, transparent (topologically deformable) domain walls are invisible to local topological probes, yet can modify the ground state degeneracy (GSD) and transmute anyons transported across them. Here, we develop an entanglement-bootstrap framework using information convex sets (ICSs) on local and noncontractible annuli to extract information about transparent domain walls directly from ground state wavefunctions at fixed points of Abelian topological phases on a torus, without taking categorical defect data as input. We derive fusion rules governing the action of anyons on extreme points of ICSs on noncontractible annuli and determine their quantum dimensions. Extreme points invariant under transport around the complementary cycle correspond one-to-one to minimum entropy states (MESs), and their number equals the GSD. The maximal topological entanglement entropy (TEE), $γ_{\rm LW}^{\max}=\log(\mathcal{D}/d_α)$, probes the net effect of walls crossing the chosen annulus, where $\mathcal{D}$ is the total quantum dimension and $d_α$ is the quantum dimension of an extreme point of its ICS. In contrast, the maximal entanglement asymmetry is $ΔS_X^{\max}=\log\mathrm{GSD}$. This value is the same for both annulus orientations and reflects the combined effect of the transparent domain walls. We further show that transparent domain walls can give rise to symmetries supported jointly on the two chosen fundamental cycles that cannot be decomposed into a product of two $1$-form symmetry operators, one supported on each cycle. By relating their action on MESs to anyon tunneling and the fusion rules, we clarify how these symmetries connect distinct ground states. Additionally, we apply the framework to Wen's plaquette model, the anisotropic dipolar toric code, and the rank-2 toric code.
Comments45 pages, 18 figures
