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Magic angle twisted bilayer graphene (MATBG) has become one of the prominenttopics in Condensed Matter during the last few years, however, fully atomisticstudies of the interacting physics are missing. In this work, we study thecorrelated insulator states of MATBG in the setting of a tight-binding model,under a perpendicular magnetic field of $0$ and $26.5$ T, corresponding to zeroand one quantum of magnetic flux per unit cell. At zero field and for dopingsof two holes ($\nu=-2$) or two electrons ($\nu=+2$) per unit cell, the Kramersintervalley coherent (KIVC) order is the ground state at the Hartree-Focklevel, although it is stabilized by a different mechanism to that in continuummodel. At charge neutrality, the spin polarized state is competitive with theKIVC due to the on-site Hubbard energy. We obtain a strongly electron-holeasymmetric phase diagram with robust insulators for electron filling and metalsfor negative filling. In the presence of magnetic flux, we predict an insulatorwith Chern number $-2$ for $\nu=-2$, a spin polarized state at chargeneutrality and competing insulators with Chern numbers $+2$ and $0$ at$\nu=+2$. The stability of the $\nu=+2$ insulators is determined by thescreening environment, allowing for the possibility of observing a topologicalphase transition.

The correlated insulators of magic angle twisted bilayer graphene at zero and one quantum of magnetic flux: a tight-binding study