强相互作用简并费米子的Monte Carlo研究：电压偏压双层石墨烯模型
Monte Carlo Study of Strongly-Interacting Degenerate Fermions: a Model for Voltage-Biased Bilayer Graphene
摘要：
我们在2+1d中建立了一个N_f=4味的相对论费米子模型，模型中的化学势μ耦合到两个符号相反的味双峰上，类似于QCD中的Isopsin化学势。这被认为是双层石墨烯中低能电子激发的有效理论，其中在层之间施加的电压确保一层上的粒子和另一层上的空穴的数量相等。该模型，然后重新制定的时空晶格交错费米子，并在没有一个符号的问题，模拟使用正统的混合蒙特卡罗算法。随着耦合强度的选择接近量子临界点认为存在的N_f<N_fc \approx 4.8，它被发现，有一个区域低于饱和的载流子密度和粒子-空穴“激子”凝聚体的规模与增加μ，更迅速地在自由场论中的相应数量，而传统的手征凝聚体强烈抑制。相应的基态被推测为一个强关联的简并费米子系统，其残余费米子表面被超流激子凝聚体扭曲。因此，该模型表现出定性不同的行为，任何模型与μ =/=0以前研究的晶格模拟。
英文摘要：
We formulate a model of N_f=4 flavors of relativistic fermion in 2+1d in the presence of a chemical potential mu coupled to two flavor doublets with opposite sign, akin to isopsin chemical potential in QCD. This is argued to be an effective theory for low energy electronic excitations in bilayer graphene, in which an applied voltage between the layers ensures equal populations of particles on one layer and holes on the other. The model is then reformulated on a spacetime lattice using staggered fermions, and in the absence of a sign problem, simulated using an orthodox hybrid Monte Carlo algorithm. With the coupling strength chosen to be close to a quantum critical point believed to exist for N_f<N_fc\approx4.8, it is found that there is a region below saturation where both the carrier density and a particle-hole "excitonic" condensate scale anomalously with increasing mu, much more rapidly that the corresponding quantities in free field theory, while the conventional chiral condensate is strongly suppressed. The corresponding ground state is speculated to be a strongly-correlated degenerate fermion system, with a remnant Fermi surface distorted by a superfluid excitonic condensate. The model thus shows qualitatively different behaviour to any model with mu=/=0 previously studied by lattice simulation.
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