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ON THE HARTREE-FOCK GROUND STATE MANIFOLD IN MAGIC ANGLE TWISTED GRAPHENE SYSTEMS.

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Title: ON THE HARTREE-FOCK GROUND STATE MANIFOLD IN MAGIC ANGLE TWISTED GRAPHENE SYSTEMS.
Authors: STUBBS, KEVIN D.1 kstubbs@berkeley.edu, BECKER, SIMON2 simon.becker@math.ethz.ch, LIN LIN1,3 linlin@math.berkeley.edu
Source: Multiscale Modeling & Simulation. 2025, Vol. 23 Issue 3, p1333-1357. 25p.
Subjects: Hartree-Fock approximation, Symmetry groups, Quantum states, Mean field theory, 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 have shown that Hartree--Fock ground states (with a positive singleparticle excitation 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. [ABSTRACT FROM AUTHOR]
Copyright of Multiscale Modeling & Simulation is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: <searchLink fieldCode="JN" term="%22Multiscale+Modeling+%26+Simulation%22">Multiscale Modeling & Simulation</searchLink>. 2025, Vol. 23 Issue 3, p1333-1357. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Hartree-Fock+approximation%22">Hartree-Fock approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+groups%22">Symmetry groups</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+states%22">Quantum states</searchLink><br /><searchLink fieldCode="DE" term="%22Mean+field+theory%22">Mean field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+breaking%22">Symmetry breaking</searchLink>
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  Label: Abstract
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  Data: 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 have shown that Hartree--Fock ground states (with a positive singleparticle excitation 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Multiscale Modeling & Simulation is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/24M1689909
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      – Code: eng
        Text: English
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        PageCount: 25
        StartPage: 1333
    Subjects:
      – SubjectFull: Hartree-Fock approximation
        Type: general
      – SubjectFull: Symmetry groups
        Type: general
      – SubjectFull: Quantum states
        Type: general
      – SubjectFull: Mean field theory
        Type: general
      – SubjectFull: Symmetry breaking
        Type: general
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      – TitleFull: ON THE HARTREE-FOCK GROUND STATE MANIFOLD IN MAGIC ANGLE TWISTED GRAPHENE SYSTEMS.
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            – D: 01
              M: 07
              Text: 2025
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              Y: 2025
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