  The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle
is believed to arise from electron correlations in topological flat bands. An
unbiased approach to this problem is highly desirable, but also particularly
challenging, given the multiple electron flavors, the topological obstruction
to defining tight binding models and the long-ranged Coulomb interactions.
While numerical simulations of realistic models have thus far been confined to
zero temperature, typically excluding some spin or valley species, analytic
progress has relied on fixed point models away from the realistic limit. Here
we present for the first time unbiased Monte Carlo simulations of realistic
models of magic angle TBG at charge-neutrality. We establish the absence of a
sign problem for this model in a momentum space approach, and describe a
computationally tractable formulation that applies even on breaking chiral
symmetry and including band dispersion. Our results include (i) the emergence
of an insulating Kramers inter-valley coherent ground state in competition with
a correlated semi-metal phase, (ii) detailed temperature evolution of order
parameters and electronic spectral functions which reveal a `pseudogap' regime,
in which gap features are established at a higher temperature than the onset of
order and (iii) predictions for electronic tunneling spectra and their
evolution with temperature. Our results pave the way towards uncovering the
physics of magic angle graphene through exact simulations of over a hundred
electrons across a wide temperature range.
