Minimal length implications on the Hartree-Fock theory

Abstract

Hartree-Fock approximation suffers from two inabilities including i) the divergence of electron Fermi velocity , and ii) existence of bandwidth not confirmed experimentally. Here, we study the effects of minimal length on the ground state energy of the electron gas in the Hartree-Fock approximation. Our results indicate that considering some mathematical terms, similar to those of used for the minimal length correction to the Hamiltonian of system, can eliminate the weaknesses of Hartree-Fock approximation. These corrections, on the other hand, can be considered as relativistic corrections of electron in solids. Physically, it is obtained that electrons in metals can be employed to test the quantum gravity scenario, if the value of its parameter ($\beta$) lies within the range of 2 to 10, depending on the used metal. Indeed, the latter addresses an upper bound on $\beta$ which is comparable with previous works meaning that these types of systems may be employed in testing quantum gravity scenarios. To overcome the infinite Fermi velocity in Hartree-Fock method, the screening potential is used based on the Lindhard theory. We also found that considering the generalized Heisenberg uncertainly leads to some additional oscillating terms in the Friedel oscillations.

10 pases, 5 figs

References in corpus (13)

• GUP parameter from quantum corrections to the Newtonian potential
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Hydrogen atom in momentum space with a minimal length
• Quantum gravity, minimum length and Keplerian orbits
• Casimir-Polder intermolecular forces in minimal length theories
• Noncommutativity, generalized uncertainty principle and FRW cosmology
• One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
• Quantum cosmology, minimal length and holography
• Generalized uncertainty principle in resonant detectors of gravitational waves
• A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas
• Effect of GUP on the Kepler problem and a variable minimal length
• Interacting Dark Side of Universe Through Generalized Uncertainty Principle