论文标题
因此（4）二维Dirac Fermions的多政治性
SO(4) multicriticality of two-dimensional Dirac fermions
论文作者
论文摘要
我们研究了（2 + 1） - 维持量的量子性多政治行为，具有八组分的dirac fermions，与两个订单参数的三胞胎耦合，这些参数为dirac群众，并以$（1,0） +（1,0） +（0,1）$表示（4）$ \ simeq $ so（3）$（3）$（3）$（3）$（3）$（3）$ so（3）$（3）$ so（3）$（3）该场理论与蜂窝上的Spin-1/2费米子或$π$ -Flux晶格有关，例如，在一侧，$ S $ - 波超导体和电荷密度波之间的过渡点，另一侧是Néel订单。此类顺序参数的两个三胞胎始终允许另外两个订单参数的共同对，可以将它们完成为五个兼容（抗强制性）顺序的最大组合。我们首先在NAMBU（粒子孔）空间中得出一个单一的转换，该空间将任何两个这样的三胞胎映射到纯粹的绝缘阶参数上。这允许人们考虑一个通用的SO（4）总体上的多政治性描述，而没有任何Nambu加倍。然后，我们继续以$4-ε$时空尺寸为单环订单来得出耦合常数的统计组流量，还允许在So（$ n_a $）$ \ times $ so（$ n_b $）下转换的更通用的订单参数集。虽然对于玻璃纤维部门的$ n_a = n_b> 2 $，并且随着费米子的脱钩，流量的固定点稳定，而Yukawa耦合到费米子很快就会通过相关的fermion口味数字$ n_f $ $ n_f $在相关范围内通过通用的固定点碰撞消除。这表明在物理案例中，临界行为替换为失控流量$ n_a = n_b = 3 $。还讨论了$ n_a \ neq n_b $的RG流量的结构，当$ n_a = 3 $和$ n_b = 1 $ in $ d = 2+1 $时，有一些非扰动论点有利于脱钩关键点的稳定性。
We study quantum multicritical behavior in a (2+1)-dimensional Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses, and transform as $(1,0) + (0,1)$ representation under the SO(4)$\simeq$SO(3)$\times$SO(3) symmetry group. This field theory is relevant to spin-1/2 fermions on honeycomb or $π$-flux lattices, for example, near the transition points between an $s$-wave superconductor and a charge-density wave, on one side, and Néel order, on the other. Two triplets of such order parameters always allow for a common pair of two other order parameters that would complete them to the maximal set of compatible (anticommuting) orders of five. We first derive a unitary transformation in the Nambu (particle-hole) space which maps any two such triplets, possibly containing some superconducting orders, onto purely insulating order parameters. This allows one to consider a universal SO(4) Gross-Neveu-Yukawa description of the multicriticality without any Nambu doubling. We then proceed to derive the renormalization-group flow of the coupling constants at one-loop order in $4-ε$ space-time dimensions, allowing also a more general set of order parameters transforming under SO($n_a$)$\times$SO($n_b$). While for $n_a=n_b > 2 $ in the bosonic sector and with fermions decoupled there is a stable fixed point of the flow, the Yukawa coupling to fermions quickly leads to its elimination by a generic fixed-point collision in the relevant range of fermion flavor numbers $N_f$. This suggests the replacement of the critical behavior by a runaway flow in the physical case $n_a=n_b=3$. The structure of the RG flow at $n_a\neq n_b$ is also discussed, and some non-perturbative arguments in favor of the stability of the decoupled critical point when $n_a=3$ and $n_b=1$ in $D=2+1$ are provided.
