论文标题
各向异性淋巴结点半法的费尔米金临界远离临界维度：精确$ 1/n_f $指数
Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents
论文作者
论文摘要
我们考虑$ d = d_l + d_q $空间尺寸在$ d_l $ demensions中线性分散，而在其余的$ d_q $尺寸中四次四边形。当受到强相互作用的影响时，这些系统易于与自发对称性断裂同时发生的半学界限转变。这样的量子临界点通过与动态阶参数字段相连的各向异性淋巴结式费物的有效场理论来描述。我们分析了与物理相关的空间维度中的通用缩放，从而将大量$ n_f $ fermion口味推广到分析控制中。通过无间隙的效率激发降水会引起非分析的自我能源校正，以占主导长波长行为的伯孔订单参数传播器。我们表明，扰动动量外壳RG会导致非宇宙，截止依赖性结果，因为它无法正确解释这种非分析结构。反过来，使用完全一般的软截止配方，我们证明了通过强制执行结果独立于截止方案来推导着穿着的骨传繁殖器的正确缩放率。使用这种软截止方法，我们将各向异性半dirac fermions $（d_l = 1 $，$ d_q = 1）$计算出确切的关键指数，以$ 1/n_f $和所有循环订单。在相对论迪拉克费米子上应用相同的方法，我们重现了通过其他方法获得的关键指数，例如共形性bootstrap ...
We consider the fermionic quantum criticality of anisotropic nodal point semimetals in $d = d_L + d_Q$ spatial dimensions that disperse linearly in $d_L$ dimensions, and quadratically in the remaining $d_Q$ dimensions. When subject to strong interactions, these systems are susceptible to semimetal-insulator transitions concurrent with spontaneous symmetry breaking. Such quantum critical points are described by effective field theories of anisotropic nodal fermions coupled to dynamical order parameter fields. We analyze the universal scaling in the physically relevant spatial dimensions, generalizing to a large number $N_f$ of fermion flavors for analytic control. Landau damping by gapless fermionic excitations gives rise to non-analytic self-energy corrections to the bosonic order-parameter propagator that dominate the long-wavelength behavior. We show that perturbative momentum shell RG leads to non-universal, cutoff dependent results, as it does not correctly account for this non-analytic structure. In turn, using a completely general soft cutoff formulation, we demonstrate that the correct IR scaling of the dressed bosonic propagator can be deduced by enforcing that results are independent of the cutoff scheme. Using this soft cutoff approach, we compute the exact critical exponents for anisotropic semi-Dirac fermions $(d_L=1$, $d_Q=1)$ to leading order in $1/N_f$, and to all loop orders. Applying the same method to relativistic Dirac fermions, we reproduce the critical exponents obtained by other methods, such as conformal bootstrap...
