格点上的强耦合石墨烯
Strongly Coupled Graphene on the Lattice
摘要：
二维碳同素异形体石墨烯近年来引起了格点场论、格点量子色动力学和蒙特卡罗计算等学科研究者的广泛关注。这种兴趣是由石墨烯中传导电子的几个显著特性引起的。例如，石墨烯在低能量下的锥形能带结构强烈地让人联想到相对论狄拉克费米子。此外，由于v_F = c/300的低费米速度，其中c是真空中的光速，石墨烯中的传导电子的物理性质与强耦合状态下的量子电动力学性质相似。反过来，这开辟了实验实现石墨烯电子相图中带隙的强关联态的前景。在这里，我们回顾了实验和理论的石墨烯的格场论研究的动机，并描述了这样的研究可能在未来几年内取得进展的方向。我们还简要介绍了石墨烯的两个主要晶格理论，六角Hubbard理论和低能Dirac理论。最后，我们描述了应用格点场论计算提取响应函数的前景，如电导率。
英文摘要：
The two-dimensional carbon allotrope graphene has recently attracted a lot of attention from researchers in the disciplines of Lattice Field Theory, Lattice QCD and Monte Carlo calculations. This interest has been prompted by several remarkable properties of the conduction electrons in graphene. For instance, the conical band structure of graphene at low energies is strongly reminiscent of relativistic Dirac fermions. Also, due the low Fermi velocity of v_F = c/300, where c is the speed of light in vacuum, the physics of the conduction electrons in graphene is qualitatively similar to Quantum Electrodynamics in a strongly coupled regime. In turn, this opens up the prospect of the experimental realization of gapped, strongly correlated states in the electronic phase diagram of graphene. Here, we review the experimental and theoretical motivations for Lattice Field Theory studies of graphene, and describe the directions that such research is likely to progress in during the next few years. We also give a brief overview of the two main lattice theories of graphene, the hexagonal Hubbard theory and the low-energy Dirac theory. Finally, we describe the prospect of extracting response functions, such as the electric conductivity, using Lattice Field Theory calculations.
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