Abstract:

In this talk, I will summarize a series of our recent works on the many-body physics in twisted bilayer graphene (TBG) and present an outlook for future theoretical studies. First, I will review the projected Coulomb Hamiltonian of TBG and derive its U(4)xU(4) and U(4) symmetries in different limits. Then, with the help of symmetries, we can write down exact eigenstates of the projected Coulomb Hamiltonian at integer fillings. These results are confirmed by numerical exact diagonalization. Given the many-body symmetries and exact ground states, we can also derive the exact charge 1, 2, 0 excitations, with Goldstone modes included. Remarkably, through charge 2 excitations, we prove the absence of Cooper pairs in the project Coulomb Hamiltonian around integer fillings. Finally, we map the TBG system to a heavy-fermion problem in a first-principles spirit. This mapping explains many previous analytical and numerical results both qualitatively and quantitatively in a simple and intuitive picture. In the end, I will discuss potential applications of the heavy-fermion model in explaining relevant experiments.