论文标题
与$ d $波配对领域的广场格子哈伯德模型中的狄拉克电子：手性海森堡普遍班级重新审视
Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
论文作者
论文摘要
我们从数值上研究了手性海森堡普遍性类别的量子关键性，其总成分总数$ n $ = 8。在存在$ d $波配对场的情况下，对方格晶格哈伯德模型进行了辅助场量子蒙特卡洛模拟，在单个粒子谱中诱导了狄拉克锥。该属性使该模型特别有趣，因为事实证明它属于Honeycomb晶格上Hubbard模型的相同通用类别，即石墨烯的规范模型，尽管单位单元格显然有所不同（例如，它们分别包含一个和两个位点）。我们确实表明，预计将发生在正方形和蜂窝晶格上的两个相变具有相同的量子关键性。我们还认为，这些模型的细节，即计数$ n $和Dirac Cones的各向异性的方式，不会更改关键指数。目前对$ n $ = 8手性海森堡通用类的指数的估计值为$ν$ = 1.05（5），$ η_ϕ $ = 0.75（4）和$η_ψ$ = 0.23（4），与先前的数值估计相比。
We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components $N$=8 in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a $d$-wave pairing field, inducing Dirac cones in the single particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, that is the canonical model for graphene, despite the unit cells being apparently different (e.g. they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting $N$ and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the $N$=8 chiral Heisenberg universality class are $ν$=1.05(5), $η_ϕ$=0.75(4), and $η_ψ$=0.23(4), which are compared with the previous numerical estimations.
