On the Hartree-Fock Ground State Manifold in Magic Angle Twisted Graphene Systems

TL;DR

This paper characterizes the Hartree-Fock ground states in magic angle twisted bilayer graphene, revealing a symmetry-driven structure and ruling out translation symmetry breaking, advancing understanding of correlated insulating phases.

Contribution

It provides a complete characterization of Hartree-Fock ground states in MATBG, including symmetry analysis and new methods to exclude translation symmetry breaking.

Findings

Hartree-Fock ground states are two ferromagnetic Slater determinants without spin and valley.

The ground state manifold is generated by a U(4) x U(4) symmetry group.

New tools are introduced to rule out translation symmetry breaking.

Abstract

Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG has shown that Hartree-Fock ground states (with a positive charge gap) can be exact many-body ground states of an idealized flat band interacting (FBI) Hamiltonian. We prove that in the absence of spin and valley degrees of freedom, the only Hartree-Fock ground states of the FBI Hamiltonian for MATBG are two ferromagnetic Slater determinants. Incorporating spin and valley degrees of freedom, we provide a complete characterization of the Hartree-Fock ground state manifold, which is generated by a ${\rm U}(4) \times {\rm U}(4)$ hidden symmetry group acting on five elements. We also introduce new tools for ruling out translation symmetry breaking in the Hartree-Fock ground state manifold, which may be of independent interest.