论文标题
通过融合电荷进行张量网络重新归一化：应用于3D晶格量表理论
Tensor network renormalization with fusion charges: applications to 3d lattice gauge theory
论文作者
论文摘要
张量网络方法是研究统计和量子系统的属性和动力学的强大而有效的工具，尤其是在一个和二维中。近年来，这些方法被应用于晶格量规理论，但这些理论仍然是$（2+1）$尺寸的挑战。在本文中，我们提出了一种新的（装饰）张量网络算法，其中张量表以融合为基础表示的晶格幅度振幅。 这具有多个优点：首先，融合基础确实使操作员测量与分层区域相关的磁通量和电荷。因此，该算法允许直接访问这些可观察物。其次，与先前使用的自旋网络基础相反，融合基础是在粗晶片下稳定的。第三，由于融合基础的层次结构，该算法确实实现了预定义的脱节，从而消除了短尺寸的纠缠。 我们将此新算法应用于定义的晶格规格理论$ \ text {su}（2）_ {\ rm k} $，并确定各个级别$ \ rm k $的弱耦合阶段。随着我们增加$ \ rm k $的级别，关键耦合$ g_c $线性减小，这表明没有连续组$ \ text {su}（2）$的连续组$ \ text {su}（2）$缺乏切除阶段。此外，我们说明了两个阶段中威尔逊循环的缩放行为。
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories, yet these theories remain a challenge in $(2+1)$ dimensions. In this article, we present a new (decorated) tensor network algorithm, in which the tensors encode the lattice gauge amplitude expressed in the fusion basis. This has several advantages: Firstly, the fusion basis does diagonalize operators measuring the magnetic fluxes and electric charges associated to a hierarchical set of regions. The algorithm allows therefore a direct access to these observables. Secondly the fusion basis is, as opposed to the previously employed spin network basis, stable under coarse graining. Thirdly, due to the hierarchical structure of the fusion basis, the algorithm does implement predefined disentangles, that remove short-scale entanglement. We apply this new algorithm to lattice gauge theories defined for the quantum group $\text{SU}(2)_{\rm k}$ and identify a weak and a strong coupling phase for various levels $\rm k$. As we increase the level $\rm k$, the critical coupling $g_c$ decreases linearly, suggesting the absence of a deconfining phase for the continuous group $\text{SU}(2)$. Moreover, we illustrate the scaling behaviour of the Wilson loops in the two phases.
