发表机构
The Chinese University of Hong Kong（香港中文大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出代数张量网络重整化（$\mathcal{R}$-TNR），将融合范畴约束融入张量网络，实现稳定的无隙不动点，并高精度提取共形场论的扇区分辨共形数据，实现拓扑自举。
AI 中文摘要
涌现广义对称性和全息原理在理解量子相变中扮演着非常重要的角色。近年来，具有广义对称性的张量网络重整化以及相应的不动点张量表述已被提出，作为在离散时空框架下重新表述共形场论的方法。然而，在该框架内仍然缺乏完整的全息表述，且当前的表述不能直接容纳通常具有模协变性的分扇区配分函数。在本工作中，我们提出了$\mathcal{R}$-TNR，它将融合范畴$\mathcal{R}$的范畴约束构建到局部张量空间中，并在Loop-TNR下保持这些约束。对于合适的$\mathcal{R}$选择，这里构造的初始张量在$\mathcal{R}$-Loop-TNR下流向稳定的无隙不动点。在Ising、三临界Ising和三态Potts共形场论示例中，广泛的初始参数范围在每个示例中都导致相同的无隙不动点。该方法按任意子扇区解析共形塔，并给出标度维度、共形自旋以及扇区分辨结构常数的大小，其精度与先前方法相比极高。这些结果实现了一种基于稳定对称拓扑序的拓扑自举，其中有限的范畴和几何输入，加上无需精细调节的初始张量，就足以恢复红外共形场论及其扇区分辨共形数据。
英文摘要
Emergent generalized symmetries and the holographic principle play very important roles in understanding quantum phase transitions. In recent years, tensor-network renormalization with generalized symmetry and the corresponding fixed-point tensor formulation have been proposed as a discrete spacetime framework for reformulating conformal field theory. Nevertheless, a complete holographic formulation within this framework is still lacking, and the current formulation does not directly accommodate sector partition functions that are modular covariant in general. In this work, we formulate $\mathcal{R}$-TNR, which builds the categorical constraints of a fusion category $\mathcal{R}$ into local tensor spaces and preserves these constraints under Loop-TNR. For suitable choices of $\mathcal{R}$, the initial tensors constructed here flow under $\mathcal{R}$-Loop-TNR to stable gapless fixed points. In the Ising, tricritical Ising, and three-state Potts conformal field theory examples, a broad range of initial parameters leads to the same gapless fixed point in each example. The method resolves conformal towers by anyon sector and yields scaling dimensions, conformal spins, and magnitudes of sector-resolved structure constants with extremely high accuracy compared to previous methods. These results realize a topological bootstrap based on stable symmetry-topological-order in which finite categorical and geometric input, together with an initial tensor that need not be fine-tuned, suffices to recover the infrared conformal field theory and its sector-resolved conformal data.
Comments82 pages, 18 figures
