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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]
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Database: Engineering Source
Description
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]
ISSN:15403459
DOI:10.1137/24M1689909