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Stability of the high-density ferromagnetic ground state of a chargeless, magnetic-dipolar, quantum Fermi liquid

S. D. Mahanti, Sudhanshu Shekhar Jha

We obtain the best upper bound for the ground-state energy of a system of chargeless fermions of mass m, spin s=1/2 , and magnetic moment mus[over ] as a function of its density in the fully spin-polarized Hartree-Fock determinantal state, specified by a prolate spheroidal plane-wave single-particle occupation function n_(k[over ]) , by minimizing the total energy E at each density with respect to the variational spheroidal deformation parameter beta(2),0< or =beta(2)< or =1 . We find that at high densities, this spheroidal ferromagnetic state is the most likely ground state of the system, but it is still unstable towards the infinite-density collapse. This optimized ferromagnetic state is shown to be a stable ground state of the dipolar system at high densities, if one has an additional repulsive short-range hardcore interaction of sufficient strength and nonvanishing range.We obtain the best upper bound for the ground-state energy of a system of chargeless fermions of mass m, spin s=1/2 , and magnetic moment mus[over ] as a function of its density in the fully spin-polarized Hartree-Fock determinantal state, specified by a prolate spheroidal plane-wave single-particle occupation function n_(k[over ]) , by minimizing the total energy E at each density with respect to the variational spheroidal deformation parameter beta(2),0< or =beta(2)< or =1 . We find that at high densities, this spheroidal ferromagnetic state is the most likely ground state of the system, but it is still unstable towards the infinite-density collapse. This optimized ferromagnetic state is shown to be a stable ground state of the dipolar system at high densities, if one has an additional repulsive short-range hardcore interaction of sufficient strength and nonvanishing range.

Physical Review EDec 5, 20074 citations

27pXX-11 Ground-state Energies of Spinless Free Fermions and Hard-core Bosons on Infinite Lattice

Wenxing Nie, Hosho Katsura, Masaki Oshikawa

日本物理学会講演概要集Mar 26, 20130 citations

The ground state of chargeless fermions with finite magnetic moment

S. D. Mahanti, Sudhanshu Shekhar Jha

We consider the ground state of a system of chargeless fermions, such as neutrinos, of mass m and magnetic moment p interacting through long-range magnetic dipole interaction, within the framework of a Hartree-Fock variational approach. At high densities the uniform paramagnetic state becomes unstable towards a ferromagnetic state with quadrupolar deformation of the Fermi surface. The exchange energy which is attractive dominates the repulsive kinetic energy. If we let the density be a variable, then above a certain density the system will collapse to an infinite density state unless another short-range interaction stops the collapse. In the case of large deformations, the possibility of a purely dipolar deformation exists.We consider the ground state of a system of chargeless fermions, such as neutrinos, of mass m and magnetic moment p interacting through long-range magnetic dipole interaction, within the framework of a Hartree-Fock variational approach. At high densities the uniform paramagnetic state becomes unstable towards a ferromagnetic state with quadrupolar deformation of the Fermi surface. The exchange energy which is attractive dominates the repulsive kinetic energy. If we let the density be a variable, then above a certain density the system will collapse to an infinite density state unless another short-range interaction stops the collapse. In the case of large deformations, the possibility of a purely dipolar deformation exists.

Journal of Physics A Mathematical and GeneralJan 24, 20065 citations

Hartree-Fock variational method for fermions

Luca Salasnich

Springer eBooksJan 1, 20200 citations

FERROMAGNETISM OF THE HUBBARD MODEL AT STRONG COUPLING IN THE HARTREE–FOCK APPROXIMATION

VOLKER BACH, Élliott H. Lieb, MARCOS V. TRAVAGLIA

As a contribution to the study of the Hartree–Fock theory, we prove rigorously that the Hartree–Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential μ) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree–Fock theory, we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.As a contribution to the study of the Hartree–Fock theory, we prove rigorously that the Hartree–Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential μ) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree–Fock theory, we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.

arXiv:cond-mat/0506695Reviews in Mathematical PhysicsJun 1, 200612 citations

The Ground State Energy of the Charged-Boson and -Fermion System at the High-Density Limit

光昭宜野座

Jan 1, 19720 citations

Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in the presence of a hard core potential: A stable ferromagnetic state

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Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in the presence of a hard core potential: A stable ferromagnetic state

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