论文标题
朝着库仑相互作用的扭曲双层石墨烯中的隐藏对称性：重新归一化组方法
Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
论文作者
论文摘要
我们开发了一个两个阶段的重新归一化组，该组将连续的哈密顿量连接到扭曲的双层石墨烯的长度比Moire Super突变峰时期的长度尺度短于Hamiltonian，仅在主动窄带中，这在距离上的有效期比Moire时期长得多。在第一阶段，库仑相互作用将费米的速度和层间隧道重新归一致，以抑制相同的sublatice与相对的Sublatice Tunneling的比率，从而接近所谓的手性手性极限。在第二阶段，层间隧道被非扰动处理。通过逐渐消除远程频带的渐进数值，确定了单粒子样色散的相对强度以及活跃窄带汉密尔顿的相互作用，从而量化了残余相关性并在最后一步中证明了强耦合方法的合理性。我们还准确地计算了投影到重新归一化狭窄带上的库仑相互作用的激子能量谱。集体模式的产生软化标志着放大的（“隐藏”）$ u（4）\ times u（4）$对称性在魔术角扭曲双层石墨烯中。
We develop a two stage renormalization group which connects the continuum Hamiltonian for twisted bilayer graphene at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only which is valid at distances much longer than the moire period. In the first stage, the Coulomb interaction renormalizes the Fermi velocity and the interlayer tunnelings in such a way as to suppress the ratio of the same sublattice to opposite sublatice tunneling, hence approaching the so-called chiral limit. In the second stage, the interlayer tunneling is treated non-perturbatively. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian is determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step. We also calculate exactly the exciton energy spectrum from the Coulomb interactions projected onto the renormalized narrow bands. The resulting softening of the collective modes marks the propinquity of the enlarged ("hidden") $U(4)\times U(4)$ symmetry in the magic angle twisted bilayer graphene.
