论文标题
Dirac Fermion系统的临界结构和紧急对称性
Critical structure and emergent symmetry of Dirac fermion systems
论文作者
论文摘要
狄拉克系统中的紧急对称性意味着该系统在某个特殊的关键点上获得了两个基本对称性的扩大。两个对称损坏相之间的连续量子临界性可以在总纽瓦瓦（GNY）模型的框架内描述。 Using the first-order $ε$ expansion in $4-ε$ dimensions, we study the critical structure and emergent symmetry of the chiral GNY model with $N_f$ flavors of four-component Dirac fermions coupled strongly to an $O(N)$ scalar field under a small $O(N)$-symmetry breaking perturbation.确定稳定的固定点后，我们计算了一般$ n $和$ n_f $的反相关长度指数和异常尺寸（玻感和费莫尼克）。此外，我们根据$ o（n）$ - gny模型讨论了$ n \ geq4 $的新兴对称性和新兴的超对称关键点。事实证明，当且仅当$ n <2n_f+4 $时，手性紧急 - $ o（n）$通用类在物理上有意义。在此前提下，小$ o（n）$ - 对称打破扰动始终与手性紧急 - $ o（n）$通用类无关。我们的研究表明，根据风味$ n_f $，Dirac Systems中的新兴对称性具有上边界$ O（2n_f+3）$。结果，出现的-o（4）$和$ o（5）$ symmetries可以在带有费米的风味$ n_f = 1 $的系统中找到，而agrent-$ o（4）$，$ o（5）$，$ o（6）$（6）$和$ o（7）$（7）$ symmeties预计将在fermion $ n_fermion $ n__f = 2 $ n_f = 2 $ n_f = 2 $ n_f = 2 $ n_f = 2 $ n_f = 2。我们的结果还表明，紧急的$ z_2 \ times o（2）\ times o（3）$对称性等等。有趣的是，在新兴的$ o（4）$通用类中，有一个超对称的临界点，可以在Fermion风味$ n_f = 1 $的系统中找到。
Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-order $ε$ expansion in $4-ε$ dimensions, we study the critical structure and emergent symmetry of the chiral GNY model with $N_f$ flavors of four-component Dirac fermions coupled strongly to an $O(N)$ scalar field under a small $O(N)$-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general $N$ and $N_f$. Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for $N\geq4$ on the basis of $O(N)$-GNY model. It turns out that the chiral emergent-$O(N)$ universality class is physically meaningful if and only if $N<2N_f+4$. On this premise, the small $O(N)$-symmetry breaking perturbation is always irrelevant in the chiral emergent-$O(N)$ universality class. Our studies show that the emergent symmetry in Dirac systems has an upper boundary $O(2N_f+3)$, depending on the flavor numbers $N_f$. As a result, the emergent-$O(4)$ and $O(5)$ symmetries are possible to be found in the systems with fermion flavor $N_f=1$, and the emergent-$O(4)$, $O(5)$, $O(6)$ and $O(7)$ symmetries are expected to be found in the systems with fermion flavor $N_f=2$. Our result also suggests some rich transitions with emergent-$Z_2\times O(2)\times O(3)$ symmetry and so on. Interestingly, in the emergent-$O(4)$ universality class, there is a supersymmetric critical point which is expected to be found in the systems with fermion flavor $N_f=1$.
