Correlated electron states in coupled quarter-flux Hofstadter layers under opposite magnetic field

We present a numerical study of a strongly correlated bilayer Hofstadter model, with properties strikingly similar to magic-angle twisted bilayer graphene (MATBG). While experiments on MATBG have revealed a variety of interesting superconducting and correlated insulating phases, a complete description of these states has been inhibited by the size of the moiré unit cell and the resultant complexity of large-scale numerical simulations. Motivated by this, we propose and analyze a lattice model containing the most important symmetries and topological features of MATBG. Namely, we study a spinful bilayer system of quarter-flux Hofstadter lattices subjected to opposite magnetic field, equipped with both local Hubbard interactions and interlayer tunneling. We explore its phase diagram using the infinite density matrix renormalization group method, finding symmetry-breaking correlated insulating states at integer filling of the lowest Hofstadter bands. We conclude by discussing its potential experimental implementation in an optical lattice system.