  Twisted bilayer graphene (TBG) provides a unique framework to elucidate the
interplay between strong correlations and topological phenomena in
two-dimensional systems. The existence of multiple electronic degrees of
freedom -- charge, spin, and valley -- gives rise to a plethora of possible
ordered states and instabilities. Identifying which of them are realized in the
regime of strong correlations is fundamental to shed light on the nature of the
superconducting and correlated insulating states observed in the TBG
experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo
simulations to solve an effective interacting lattice model for TBG at charge
neutrality. Besides the usual cluster Hubbard-like repulsion, this model also
contains an assisted hopping interaction that emerges due to the non-trivial
topological properties of TBG. Such a non-local interaction fundamentally
alters the phase diagram at charge neutrality, gapping the Dirac cones even for
infinitesimally small interaction. As the interaction strength increases, a
sequence of different correlated insulating phases emerge, including a quantum
valley Hall state with topological edge states, an intervalley-coherent
insulator, and a valence bond solid. The charge-neutrality correlated
insulating phases discovered here provide the sought-after reference states
needed for a comprehensive understanding of the insulating states at integer
fillings and the proximate superconducting states of TBG.
