Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology
Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology
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DOI：
10.1103/physrevd.107.034501
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发表时间：
2022-07
影响因子：
5
通讯作者：
Nicholas Sale;B. Lucini;Jeffrey Giansiracusa
中科院分区：
文献类型：
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作者：
Nicholas Sale;B. Lucini;Jeffrey Giansiracusa
我们研究了持久同源性（拓扑数据分析的工具）的使用，作为以规范不变的方式检测和定量描述 $\mathrm{SU}(2)$ 晶格规范理论中的中心涡旋的方法。我们通过检测在解除限制阶段使用扭曲边界条件显式插入的涡旋，为我们的方法对涡旋的敏感性提供了证据。这启发了解禁相变的新阶段指标的定义。我们还使用简单的 $k$-最近邻分类器构建了一个不参考扭曲边界条件的相位指示器。对两个基于持久性的指标的有限尺度分析可以准确估计解约束相变的临界 $\beta$ 和相关长度 $\nu$ 的临界指数。
We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in $\mathrm{SU}(2)$ lattice gauge theory in a gauge-invariant manner. We provide evidence for the sensitivity of our method to vortices by detecting a vortex explicitly inserted using twisted boundary conditions in the deconfined phase. This inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a simple $k$-nearest neighbours classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical $\beta$ and critical exponent of correlation length $\nu$ of the deconfinement phase transition.