Exact ground state of interacting electrons in magic angle graphene (2312.15314v1)
Abstract: One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene (TTG) systems with equal twist angles. We identify symmetries of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-$\theta$ and Weierstrass-$\wp$ functions.
- Spectral characterization of magic angles in twisted bilayer graphene. Phys. Rev. B, 103(16):165113, 2021.
- Mathematics of magic angles in a model of twisted bilayer graphene. Prob. Math. Phys., 3(1):69–103, 2022.
- Chiral limit of twisted trilayer graphene. arXiv:2308.10859, 2023.
- Fine structure of flat bands in a chiral model of magic angles. arXiv:2208.01628, 2022.
- Degenerate flat bands in twisted bilayer graphene. arXiv:2306.02909, 2023.
- Integrability in the chiral model of magic angles. Communications in Mathematical Physics, 403(2):1153–1169, October 2023.
- Twisted bilayer graphene. III. Interacting Hamiltonian and exact symmetries. Phys. Rev. B, 103(20):205413, 2021.
- R. Bistritzer and A. H. MacDonald. Moire bands in twisted double-layer graphene. Proceedings of the National Academy of Sciences, 108(30):12233–12237, 2021.
- Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene. 124(16):166601.
- Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling. Phys. Rev. X, 10(3):031034, 2020.
- Simple derivation of moiré-scale continuous models for twisted bilayer graphene. Phys. Rev. B, 107:155403, Apr 2023.
- Semiclassical analysis of two-scale electronic hamiltonians for twisted bilayer graphene, 2023.
- Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature, 556(7699):80–84, mar 2018.
- Unconventional superconductivity in magic-angle graphene superlattices. Nature, 556(7699):43–50, 2018.
- Symmetry breaking and skyrmionic transport in twisted bilayer graphene. Phys. Rev. B, 101(16), apr 2020.
- Symmetry-broken chern insulators and rashba-like landau-level crossings in magic-angle bilayer graphene. Nat. Phys., 17(6):710–714, mar 2021.
- Interacting models for twisted bilayer graphene: A quantum chemistry approach. Phys. Rev. B, 107(23):235123, 2023.
- Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature, 573(7772):91–95, jul 2019.
- Tosio Kato. Perturbation theory for linear operators; 2nd ed. Grundlehren der mathematischen Wissenschaften : a series of comprehensive studies in mathematics. Springer, Berlin, 1976.
- Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality. Phys. Rev. Res., 3(1), jan 2021.
- Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality. Phys. Rev. Res., 3(1):013033, 2021.
- Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature, 574(7780):653–657, oct 2019.
- Interacting electrons. Cambridge University Press, 2016.
- A Mielke. Exact ground states for the Hubbard model on the Kagome lattice. 25(16):4335–4345.
- A Mielke. Ferromagnetic ground states for the Hubbard model on line graphs. 24(2):L73–L77.
- A Mielke. Ferromagnetism in the Hubbard model on line graphs and further considerations. 24(14):3311–3321.
- David Mumford and C. Musili. Tata Lectures on Theta. Modern Birkhäuser Classics. Birkhäuser, 2007.
- Magic angles in equal-twist trilayer graphene. Phys. Rev. B, 108:L081124, Aug 2023.
- Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene. Phys. Rev. Lett., 127(14):147203, 2021.
- Hofstadter subband ferromagnetism and symmetry-broken chern insulators in twisted bilayer graphene. Nat. Phys., 17(4):478–481, jan 2021.
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science, 367(6480):900–903, February 2020.
- Efficient simulation of moire materials using the density matrix renormalization group. Phys. Rev. B, 102(20):205111, 2020.
- Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications, Inc., Mineola, first edition, 1996.
- Origin of magic angles in twisted bilayer graphene. Phys. Rev. Let., 122(10):106405, 2019.
- Charles Van Loan. Computing the CS and the generalized singular value decompositions. Numer. Math., 46(4):479–491, 1985.
- Bistritzer-MacDonald dynamics in twisted bilayer graphene. Journal of Mathematical Physics, 64(3):031502, March 2023.
- Existence of the first magic angle for the chiral model of bilayer graphene. J. Math. Phys., 62(9):091502, 2021.
- Collective excitations of quantum anomalous hall ferromagnets in twisted bilayer graphene. Phys. Rev. Lett., 124(4), jan 2020.
- Nature of the Correlated Insulator States in Twisted Bilayer Graphene. Phys. Rev. Lett., 124(9):097601, 2020.
- Mengxuan Yang. Flat Bands and High Chern Numbers in Twisted Multilayer Graphene. arXiv:2303.00103, 2023.
- Tuning superconductivity in twisted bilayer graphene. Science, 363(6431):1059–1064, mar 2019.
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