单层石墨烯中手征对称性破缺的紧和非紧U（1）格点规范理论强耦合展开
Chiral Symmetry Breaking in Monolayer Graphene by Strong Coupling Expansion of Compact and Non-compact U(1) Lattice Gauge Theories
摘要：
由于真空悬浮的石墨烯中库仑耦合强度的有效增强，该系统可以通过在费米子谱中形成能隙而从半金属转变为绝缘体。这种现象类似于强耦合相对论场论中的手征对称性自发破缺。我们采用U（1）格点规范理论作为石墨烯的有效模型，研究了强耦合机制下石墨烯上的这种“手征对称性破缺”和相关的集体激发。紧的和非紧的U（1）规范作用量公式在强耦合极限下都表现出手征对称性破缺，手征凝聚体（激子凝聚体）的大小相等，而在强耦合展开下它们开始偏离次领先阶。相位和振幅波动的序参量也进行了研究：特别是，一个质量公式的伪Nambu-Goldstone模式（$π$ -激子），这是类似于Gell-Mann-Oakes-Renner关系的π介子在量子色动力学（QCD），是来自轴向Ward-Takahashi恒等式。为了检查有效场论描述的适用性，通过将U（1）规范理论的晶格间距与石墨烯的原始蜂窝晶格的晶格间距相识别来估计费米子和玻色子激发的典型能量标度。
英文摘要：
Due to effective enhancement of the Coulomb coupling strength in the vacuum-suspended graphene, the system may turn from a semimetal into an insulator by the formation of a gap in the fermionic spectrum. This phenomenon is analogous to the spontaneous breaking of chiral symmetry in the strong-coupling relativistic field theories. We study this "chiral symmetry breaking" and associated collective excitations on graphene in the strong coupling regime by taking U(1) lattice gauge theory as an effective model for graphene. Both compact and non-compact formulations of the U(1) gauge action show chiral symmetry breaking with equal magnitude of the chiral condensate (exciton condensate) in the strong coupling limit, while they start to deviate from the next-to-leading order in the strong coupling expansion. Phase and amplitude fluctuations of the order parameter are also investigated: in particular, a mass formula for the pseudo-Nambu--Goldstone mode ($π$-exciton), which is analogous to Gell-Mann--Oakes--Renner relation for the pion in quantum chromodynamics (QCD), is derived from the axial Ward-Takahashi identity. To check the applicability of the effective field theory description, typical energy scales of fermionic and bosonic excitations are estimated by identifying the lattice spacing of the U(1) gauge theory with that of the original honeycomb lattice of graphene.
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