Employing the recently developed momentum-space quantum Monte Carlo scheme, we study the dynamic response of single-particle and collective excitations in realistic continuum models of twisted bilayer graphene. At charge neutrality with small flat-band dispersion, this unbiased numerical method reveals single-particle spectra and collective excitations at finite temperature. Single-particle spectra indicate that repulsive interactions push the fermion spectral weight away from the Fermi energy and open up an insulating gap. The spectra of collective excitations suggest an approximate valley $\text{SU}\left(2\right)$ symmetry. At low energy, long-lived valley waves are observed, which resemble spin waves of Heisenberg ferromagnetism. At high energy, these sharp modes quickly become overdamped, when their energy reaches the fermion particle-hole continuum.

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• Mesoscopics
• Graphene
• Strongly correlated systems
• Quantum Monte Carlo