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

arXiv · (2024)

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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 U(4) × 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.
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要点】:本文证明了在忽略自旋和谷自由度的情况下,魔角扭曲双层石墨烯系统中的Hartree-Fock基态只能是两种铁磁 Slater 行列式,并完整描述了包含自旋和谷自由度的基态流形,揭示了其背后的U(4) × U(4)隐藏对称性。

方法】:作者通过理论推导和对称性分析,研究了魔角扭曲双层石墨烯系统中的Hartree-Fock基态,并提出了新的方法来判断基态流形中是否存在平移对称性破缺。

实验】:本文未涉及具体的实验操作,但理论结果与MATBG在半填充情况下表现出相关绝缘相行为的实验现象相符合。数据集名称未提及。