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Integrability in the chiral model of magic angles

Mathematical Physics 2023-06-02 v3 Materials Science Strongly Correlated Electrons math.MP Spectral Theory Quantum Physics

Abstract

Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer--MacDonald Hamiltonian exhibits a flat band at energy zero. We compute the sums over powers of (complex) magic angles and use that to show that the set of magic angles is infinite. We also provide a new proof of the existence of the first real magic angle, showing also that the corresponding flat band has minimal multiplicity for the simplest possible choice of potentials satisfying all symmetries. These results indicate (though do not prove) a hidden integrability of the chiral model.

Cite

@article{arxiv.2208.01620,
  title  = {Integrability in the chiral model of magic angles},
  author = {Simon Becker and Tristan Humbert and Maciej Zworski},
  journal= {arXiv preprint arXiv:2208.01620},
  year   = {2023}
}

Comments

Simplification and strenghtening of trace formula

R2 v1 2026-06-25T01:25:23.839Z