相关论文: Unrestricted Hartree-Fock theory of Wigner crystal…
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles…
We use Density Functional Theory to study interacting spinless electrons on a one-dimensional quantum ring in the density range where the system undergoes Wigner crystallization. The Wigner transition leads to a drastic ``collective''…
It is known that a gas of electrons in a uniform neutralizing background can crystallize and form a lattice if the electron density is less than a critical value. This crystallization may have two- or three-dimensional structure. Since the…
Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar…
The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their…
We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We…
Wigner crystals (WC) are electronic phases peculiar to low-density systems, particularly in the uniform electron gas. Since its introduction in the early twentieth century, this model has remained essential to many aspects of electronic…
We calculate the Hartree-Fock energy of a density-wave in a spin polarized two-dimensional electron gas using a short-range repulsive interaction. We find that the stable ground state for a short-range potential is always either the…
We consider the ground state of the homogeneous electron gas and we prove that a Hartree-Fock solution, motivated by previous simulations, has lower energy than the Fermi gas in the large density limit. This solution is a metallic phase :…
We present a calculation of the imaginary part of the polarizability of a Wigner crystal using the Fluctuation-Dissipation theorem. The oscillations of the localized electrons about their equilibrium positions are treated in the harmonic…
Precise solutions of the Hartree-Fock equations for the ground state of the hydrogen molecule are obtained for a wide range of internuclear distances R by means of a two-dimensional fully numerical mesh computational method. The spatial…
We consider the three-dimensional electron gas confined by a strictly two-dimensional homogeneous positive charge density at $z=0$. Within the Hartree-Fock approximation, we study the mode structure in the confined direction in the metallic…
The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions on the linearised operator. Perturbations are moreover…
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single $\delta$ barrier. We…
This article is concerned with the numerical simulations of perfect crystals. We study the rate of convergence of the reduced Hartree-Fock (rHF) model in a supercell towards the periodic rHF model in the whole space. We prove that, whenever…
We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a…
The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters $K_{\rho}$ and $v_{\sigma}$. In this paper we discuss microscopic estimates of the values of these…
Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree-Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave…
In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function ($\mathcal{W}$) thanks to a universal functional transformation ($\mathcal{F}$), whose formal existence is akin to that of…
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this…