Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality
Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality
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DOI：
10.1103/physrevb.100.134507
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发表时间：
2019-07
影响因子：
3.7
通讯作者：
Bernhard Ihrig;N. Zerf;P. Marquard;I. Herbut;M. Scherer
中科院分区：
文献类型：
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作者：
Bernhard Ihrig;N. Zerf;P. Marquard;I. Herbut;M. Scherer
阿贝尔希格斯模型是超导转变和安德森-希格斯机制的教科书示例，并且已成为描述解禁量子临界性的关键。我们研究了 $4-\epsilon$ 展开中具有 $n$ 复标量场的阿贝尔希格斯模型，以前所未有的四循环顺序，发现临界点和双临界点的湮灭发生在临界数量 $n_c \approx 182.95\left(1 - 1.752\epsilon + 0.798 \epsilon^2 + 0.362\epsilon^3\right) + \mathcal{O}\left(\epsilon^4\right)\nonumber$。因此，在 $n_c$ 以下，转换从第二阶变为第一阶。恢复序列以提取三维结果为临界 $n_c(d=3)$ 提供了强有力的证据，该临界值显着低于主序值，但 $n_c$ 的估计值分布广泛。推测二维和四维之间的重正化群流的拓扑，我们获得 $n_c(d)$ 的平滑插值函数，并找到 $n_c(3)\approx 12.2\pm 3.9$ 作为我们在三个维度上的最佳估计。最后，我们讨论 $n_c$ 以下发生的米兰斯基标度，并评论解禁量子跃迁的弱一阶行为的影响。我们预测对应于不同 $n$ 的解禁量子跃迁之间会出现长度尺度的层次结构。
The abelian Higgs model is the textbook example for the superconducting transition and the Anderson-Higgs mechanism, and has become pivotal in the description of deconfined quantum criticality. We study the abelian Higgs model with $n$ complex scalar fields at unprecedented four-loop order in the $4-\epsilon$ expansion and find that the annihilation of the critical and bicritical points occurs at a critical number of $n_c \approx 182.95\left(1 - 1.752\epsilon + 0.798 \epsilon^2 + 0.362\epsilon^3\right) + \mathcal{O}\left(\epsilon^4\right)\nonumber$. Consequently, below $n_c$, the transition turns from second to first order. Resummation of the series to extract the result in three-dimensions provides strong evidence for a critical $n_c(d=3)$ which is significantly below the leading-order value, but the estimates for $n_c$ are widely spread. Conjecturing the topology of the renormalization group flow between two and four dimensions, we obtain a smooth interpolation function for $n_c(d)$ and find $n_c(3)\approx 12.2\pm 3.9$ as our best estimate in three dimensions. Finally, we discuss Miransky scaling occurring below $n_c$ and comment on implications for weakly first-order behavior of deconfined quantum transitions. We predict an emergent hierarchy of length scales between deconfined quantum transitions corresponding to different $n$.