DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene
DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene
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DOI：
10.21468/scipostphyscore.3.2.015
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发表时间：
2020-04
期刊：
影响因子：
--
通讯作者：
P. Eugenio;Ceren B. Daug
中科院分区：
文献类型：
--
作者：
P. Eugenio;Ceren B. Daug
通过使用最低朗道能级 (LLL) 波函数，研究了占据相反（或相似）拓扑量子数带 (Chern$=\pm1$) 且具有平坦色散的电子之间的强相互作用。更准确地说，我们确定半填充时两种情况的基态：(i) LLL 具有相反的磁场符号，因此具有相反的陈数； (ii) 具有相同磁场的 LLL。在第一个场景中——我们认为这是一个受扭曲双层石墨烯的手性对称连续介质模型启发的玩具模型——相反的 Chern LLL 是 Kramer 对，因此存在时间反转对称性 ($\mathbb{Z}_2$)。打开排斥相互作用会驱动系统自发地打破时间反转对称性——一种由每个 LLL 轨道一个粒子描述的量子反常霍尔态，要么全部为正陈 $|++\cdots+>$，要么全部为负 $|--\cdots->$。相反，如果在类似陈数的电子之间发生相互作用，则基态是 $SU(2)$ 铁磁体，总自旋指向任意方向，就像 $\nu=1$ spin-$\frac{1}{2}$ 量子霍尔铁磁体一样。这两种情况的基态及其一些激发都经过分析论证，并通过密度矩阵重整化群（DMRG）和精确对角化进一步补充。
Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern$=\pm1$), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL's with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL's with the same magnetic field. In the first scenario -- which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene -- the opposite Chern LLL's are Kramer pairs, and thus there exists time-reversal symmetry ($\mathbb{Z}_2$). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry -- a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern $|++\cdots+>$ or all negative $|--\cdots->$. If instead, interactions are taken between electrons of like-Chern number, the ground state is an $SU(2)$ ferromagnet, with total spin pointing along an arbitrary direction, as with the $\nu=1$ spin-$\frac{1}{2}$ quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.