蜂窝格子上的二维哈伯德模型
The 2D Hubbard model on the honeycomb lattice
摘要：
我们考虑蜂窝晶格上的二维哈伯德模型，作为存在屏蔽库仑相互作用的单层石墨烯片的模型。在半填充和足够弱的耦合下，计算了自由能和基态能，并以收敛级数的形式构造了零温下的关联函数，利用构造性费米子重整化群方法证明了分析性.我们表明，相互作用产生修改的费米速度和波函数重整化，而不改变渐近红外性质的模型相对于未扰动的非相互作用的情况下，这排除了超导或磁不稳定性的可能性，在基态。我们还证明了相关验证沃德恒等式类似于一个无质量狄拉克费米子，渐近可忽略的修正和重整化的电荷速度。
英文摘要：
We consider the 2D Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analiticity is proved by making use of constructive fermionic renormalization group methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the ground state. We also prove that the correlations verify a Ward Identity similar to the one for massless Dirac fermions, up to asymptotically negligible corrections and a renormalization of the charge velocity.
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