论文标题
拓扑半学的红外固定点
Infrared fixed points of higher-spin fermions in topological semimetals
论文作者
论文摘要
我们确定由哈密顿式$ h = \ textbf {p} \ cdot \ cdot \ textbf {j} $与线性频段交叉中的三维拓扑半学分，其中$ \ textbf {p} $ moment and moment and for textbf { $ J \ GEQ 3/2 $。尽管由于状态消失的密度，弱的短距离相互作用在跨点无关，但弱的远程库仑相互作用导致条带结构的重新归一化。使用自洽的扰动重归其化组方法，我们表明类型$ \ textbf {p} \ cdot \ textbf {j} $的频段交叉是$ j \ leq 7/2 $不稳定的。取而代之的是，通过在立方晶体对称性，带拓扑和相互作用效果之间引人入胜的相互作用，该系统被各种红外固定点所吸引。我们还揭示了一般$ j $的高旋转费用的其他几个属性，例如费米昂自我能量和自由能之间的关系，或者消失了重新规范化的电荷。 $ \ text {o}（3）$对称固定点由同等手性韦尔米斯组成的稳定稳定，对于$ j \ leq 7/2 $，对于所有$ j $，很可能。然后，我们详细介绍了$ j = 5/2 $的丰富固定点结构。我们找到了带有增强的$ \ text {o}（3）对称的其他有吸引力的固定点，它们既容纳了出现的Weyl或无质量的Dirac Fermions，并确定了令人困惑的，红外的稳定，各向异性固定点，而没有与已知情况相比，而没有增强的对称性，而对对称性的对称为$ J = 3/2 $。
We determine the fate of interacting fermions described by the Hamiltonian $H=\textbf{p}\cdot \textbf{J}$ in three-dimensional topological semimetals with linear band crossing, where $\textbf{p}$ is momentum and $\textbf{J}$ are the spin-$j$ matrices for half-integer pseudospin $j\geq 3/2$. While weak short-range interactions are irrelevant at the crossing point due to the vanishing density of states, weak long-range Coulomb interactions lead to a renormalization of the band structure. Using a self-consistent perturbative renormalization group approach, we show that band crossings of the type $\textbf{p}\cdot \textbf{J}$ are unstable for $j\leq 7/2$. Instead, through an intriguing interplay between cubic crystal symmetry, band topology, and interaction effects, the system is attracted to a variety of infrared fixed points. We also unravel several other properties of higher-spin fermions for general $j$, such as the relation between fermion self-energy and free energy, or the vanishing of the renormalized charge. An $\text{O}(3)$ symmetric fixed point composed of equal chirality Weyl fermions is stable for $j\leq 7/2$ and very likely so for all $j$. We then explore the rich fixed point structure for $j=5/2$ in detail. We find additional attractive fixed points with enhanced $\text{O}(3)$ symmetry that host both emergent Weyl or massless Dirac fermions, and identify a puzzling, infrared stable, anisotropic fixed point without enhanced symmetry in close analogy to the known case of $j=3/2$.
