Entropic order parameters for the phases of QFT
Entropic order parameters for the phases of QFT
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DOI：
10.1007/jhep04(2021)277
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发表时间：
2021-04-29
影响因子：
5.4
通讯作者：
Pontello, Diego
中科院分区：
文献类型：
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作者：
Casini, Horacio;Huerta, Marina;Pontello, Diego
我们提出了熵序参数，捕捉广义对称性和相位的QFT的物理。我们这样做，通过一个简单的属性（可加性和哈格对偶）的网络连接到时空区域的运营商代数的分析。我们观察到，不同类型的对称性与这些属性在不同的非平凡拓扑结构的区域中的破坏相关联。当这种拓扑是连通的时，我们证明了非局部生成算子生成一个阿贝尔对称群，并且它们的对易关系是固定的。序参数与面积法的存在，如威尔逊环的限制阶段，或't Hooft循环的双希格斯阶段，表明意味着存在一个以上的可能选择的代数相同的基础理论。一个自然的熵序参数产生这种非唯一性。我们显示方面的理论与广义对称性的这些熵序参数的阶段。特别是，在这种方法中，常数和面积定律的双序和无序参数之间的连接是透明的，从共形对称性所产生的新的约束被揭示，狄拉克量子化条件（及其推广）的代数起源进行了描述。在这种方法中的一个新的工具是熵的确定性关系所满足的双相对熵与互补区域，定量地涉及统计的有序和无序参数。
We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT's. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras attached to space-time regions. We observe that different types of symmetries are associated with the breaking of these properties in regions of different non-trivial topologies. When such topologies are connected, we show that the non locally generated operators generate an Abelian symmetry group, and their commutation relations are fixed. The existence of order parameters with area law, like the Wilson loop for the confinement phase, or the 't Hooft loop for the dual Higgs phase, is shown to imply the existence of more than one possible choice of algebras for the same underlying theory. A natural entropic order parameter arises by this non-uniqueness. We display aspects of the phases of theories with generalized symmetries in terms of these entropic order parameters. In particular, the connection between constant and area laws for dual order and disorder parameters is transparent in this approach, new constraints arising from conformal symmetry are revealed, and the algebraic origin of the Dirac quantization condition (and generalizations thereof) is described. A novel tool in this approach is the entropic certainty relation satisfied by dual relative entropies associated with complementary regions, which quantitatively relates the statistics of order and disorder parameters.