Realizing Correlated Electron States of Twisted Bilayer Graphene in an Optical Lattice Model

Experiments on magic-angle twisted bilayer graphene (MATBG) have found that it hosts a plethora of strongly correlated phases as well as superconductivity. Owing to the size of the moiré unit cell and the resultant complexity of unbiased numerical simulation, a complete theoretical understanding of these phases remains an outstanding challenge. Here, we propose and numerically investigate a bilayer optical lattice model that captures the essential elements of MATBG. Namely, we study a spinful bilayer system of quarter-flux Hofstadter lattices subjected to opposite magnetic fields, equipped with both local Hubbard interactions and interlayer tunneling. We explore its phase diagram using the infinite density matrix renormalization group, finding numerous correlated phases at integer and fractional fillings of the lowest Hofstadter bands including phases analogous to the generalized quantum Hall ferromagnets of MATBG. We conclude by providing an experimental blueprint for realizing this model in near-term optical lattice setups.