Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene

We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moir\'e band filling $\nu=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moir\'e Brillouin zone. The low-energy collective modes are faithfully described by a model with a local $SU(8)$ degree of freedom in each moir\'e unit cell that we identify as the direct product of spin, valley, and an orbital pseudospin. Apart from spin and valley-wave modes, the collective mode spectrum includes a low-energy intra-flavor exciton mode associated with transitions between flat valence and conduction band orbitals.