DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

• DOI: 10.21468/scipostphyscore.3.2.015
• Publication Date: 2020-12-09T07:24:23Z
• Authors: Paul Eugenio; Ceren Dag
• Keywords: Bilayer graphene

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 sign magnetic field, therefore Chern number; (ii) same field. In first scenario -- which argue to be a toy model inspired chirally symmetric continuum twisted bilayer graphene Kramer pairs, thus there exists time-reversal symmetry ($\mathbb{Z}_2$). Turning on repulsive drives system spontaneously break anomalous Hall state described one particle per LLL orbital, either all positive $|++\cdots+>$ or negative $|--\cdots->$. If instead, taken like-Chern number, is an $SU(2)$ ferromagnet, total spin pointing along arbitrary direction, as $\nu=1$ spin-$\frac{1}{2}$ ferromagnet. The some their excitations both these argued analytically, further complimented density matrix renormalization group (DMRG) exact diagonalization.