  We address the precise determination of the phase diagram of magic angle
twisted bilayer graphene under hydrostatic pressure within a self-consistent
Hartree-Fock method in real space, including all the remote bands of the
system. We further present a novel algorithm that maps the full real-space
density matrix to a reduced density matrix based on a $SU(4)$ symmetry of
sublattice and valley degrees of freedom. We find a quantum critical point
between a nematic and a Kekul\'e phase, and show also that our microscopic
approach displays a strong particle-hole asymmetry in the weak coupling regime.
We arrive then at the prediction that the superconductivity should be
Ising-like in the hole-doped nematic regime, with spin-valley locking, and
spin-triplet in the electron-doped regime.
