arXiv:1203.5016 · Journal of Mathematical Physics

Ground state properties of graphene in Hartree-Fock theory

Christian Hainzl, Mathieu Lewin B, Christof Sparber

Published Sep 1, 2012• 14 citations

Abstract

We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non-perturbative.

DOI: 10.1063/1.4750049

Related papers

Hartree-Fock ground state of the composite fermion metal

Within the Hartree-Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the singleparticle energy at the Fermi momentum. It is shown that the Hartree-Fock result brings no corrections to the RPA Fermi velocity. 1

Jan 1, 19950 citations

HARTREE–FOCK GROUND STATE OF THE COMPOSITE FERMION METAL

Piotr Sitko, Lucjan Jacak

Within the Hartree–Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the single-particle exchange at the Fermi momentum. It is shown that the Hartree–Fock result brings no corrections to the RPA Fermi velocity.

arXiv:cond-mat/9506018Modern Physics Letters BJun 20, 19950 citations

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

Kevin D. Stubbs, Simon Becker, Lin Lin

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 single-particle 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 [Formula: see text] 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.

arXiv:2403.19890Multiscale Modeling and SimulationAug 28, 20253 citations

Hartree-Fock approximation for non-Coulomb interactions in three and two-dimensional systems

Vlad-Mihai Ene, Ilinca Lianu, I. Grosu

We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate analytical results for the particle energy, the particle velocity, the ground state energy of the system as well as the momentum dependent density of states . The previous classical results for the Coulombian case were reobtained as particular cases.

arXiv:2408.14967Physics Letters ANov 17, 20241 citation

Rigorous construction of ground state correlations in graphene: Renormalization of the velocities and Ward identities

Alessandro Giuliani, Vieri Mastropietro

We consider the two-dimensional Hubbard model on the honeycomb lattice, as a model for single-layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground-state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its noninteracting value and turns out to be isotropic; as a consequence, the Dirac cones are isotropic at low energies. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast to the predictions based on relativistic or continuum approximations.

arXiv:0901.4867Physical Review BMay 20, 200931 citations

THERMAL PROPERTIES AND GROUND STATE ENERGY SHIFT OF CHARGED ANYONS

J.Y. Kim, Yun Soo Myung, S.H. Yi

We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.

International Journal of Modern Physics AAug 10, 19940 citations