论文标题
量子关键子延伸的信息几何形状：相关，边际和无关的操作员
Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators
论文作者
论文摘要
我们分析了沿理论空间临界亚曼叶的量子度量的热力学极限。在文献中先前已知的各种结果的基础上，我们将其奇异行为与正常方向联系起来，正常方向与重新归一化群体中的相关操作员自然相关。我们以信息理论和差异几何形状的语言制定这些结果。我们通过XY和Haldane模型的范式实例来体现我们的理论，在该模型中，指向临界子序的正常方向被视为准确是指标具有奇异行为的指标，而对于它的切线而言，这些方向消失了 - 这些方向在于度量的核心。
We analyze the thermodynamical limit of the quantum metric along critical submanifolds of theory space. Building upon various results previously known in the literature, we relate its singular behavior to normal directions, which are naturally associated with relevant operators in the renormalization group sense. We formulate these results in the language of information theory and differential geometry. We exemplify our theory through the paradigmatic examples of the XY and Haldane models, where the normal directions to the critical submanifolds are seen to be precisely those along which the metric has singular behavior, while for the tangent ones it vanishes -- these directions lie in the kernel of the metric.
