Self-consistent Hartree-Fock Approach Research Articles

Self-consistent Hartree-Fock approach to many-body localization

In this work, we develop a self-consistent Hartree-Fock approach to theoretically study the far-from-equilibrium quantum dynamics of interacting fermions, and apply this approach to explore the onset of many-body localization (MBL) in these systems. We investigate the dynamics of a state with a nonequilibrium density profile; we find that at weak disorder the density profile equilibrates rapidly, whereas for strong disorder it remains frozen on the accessible timescales. We analyze this behavior in terms of the Hartree-Fock self-energy. At weak disorder the self-energy fluctuates strongly and can be interpreted as a self-consistent noise process. By contrast, at strong disorder the self-energy evolves with a few coherent oscillations which cannot delocalize the system. Accordingly, the non-equilibrium site-resolved spectral function shows a broad spectrum at weak disorder and sharp spikes at strong disorder. Our Hartree-Fock theory incorporates spatial fluctuations and rare-region effects. As a consequence, we find subdiffusive relaxation in random systems; but, when the system is subjected to weak quasi-periodic potentials, the subdiffusive response ceases to exist, as rare region effects are absent in this case. This self-consistent Hartree-Fock approach can be regarded as a relatively simple theory that captures much of the MBL phenomenology.

Self-consistent Hartree-Fock approach for interacting bosons in optical lattices

A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott-insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.

Self-Consistent Hartree–Fock Approach to Electronic Structure of Endohedral Fullerene Ar@C60

Results of the first self-consistent calculation of electronic structure of endohedral fullerenes within the Hartree-Fock approximation are presented. The case study is Ar@C60. A phenomenon of the significant hybridization of the valent shell of the confined atom due to the presence of the fullerene core is observed. It is shown that the exchange interaction between all electrons of the endohedral compound plays a significant role in the process of hybridization. It is also shown that the hybridization of the atomic valent shell leads to the significant charge redistribution inside the endohedral compound.

Theoretical study of interacting hole gas inp-doped bulk III-V semiconductors

We study the homogeneous interacting hole gas in $p$-doped bulk III-V semiconductors. The structure of the valence band is modelled by Luttinger's Hamiltonian in the spherical approximation, giving rise to heavy and light hole dispersion branches, and the Coulomb repulsion is taken into account via a self-consistent Hartree-Fock treatment. As a nontrivial feature of the model, the self-consistent solutions of the Hartree-Fock equations can be found in an almost purely analytical fashion, which is not the case for other types of effective spin-orbit coupling terms. In particular, the Coulomb interaction renormalizes the Fermi wave numbers for heavy and light holes. As a consequence, the ground state energy found in the self-consistent Hartree-Fock approach and the result from lowest-order perturbation theory do not agree. We discuss the consequences of our observations for ferromagnetic semiconductors, and for the possible observation of the spin-Hall effect in bulk $p$-doped semiconductors. Finally, we also investigate elementary properties of the dielectric function in such systems.

High-spin intruder states in thefp-shell nuclei and isoscalar proton-neutron correlations

We perform a systematic theoretical analysis of fully-aligned, high-spin ${f}_{7/2}^{n}$ seniority isomers and ${d}_{3/2}^{\ensuremath{-}1}{f}_{7/2}^{n+1}$ intruder states in the $A~44$ nuclei from the lower-$\mathit{fp}$ shell. The configuration-interaction calculations, based on the nuclear shell model, are performed in the full $\mathit{sdfp}$ configuration space allowing $1p$-$1h$ cross-shell excitations. The density functional theory calculations are carried out within the self-consistent Hartree-Fock approach with the Skyrme energy functional that reproduces empirical Landau parameters. While there is a nice agreement between experimental and theoretical relative energies of fully-aligned states in $N>Z$ nuclei, this is no longer the case for the $N=Z$ systems. The remaining deviation from the data is attributed to the isoscalar proton-neutron correlations. It is also demonstrated that the Coulomb corrections at high spins noticeably depend on the choice of the energy density functional.

Electron–hole generations: a numerical approach to interacting fermion systems

A new approach, motivated by Fock space localization, for constructing a reduced many-particle Hilbert space is proposed and tested. The self-consistent Hartree–Fock approach is used to obtain a single-electron basis from which the many-particle Hilbert space is constructed. For a given size of the truncated many particle Hilbert space, only states with the lowest number of particle–hole excitations are retained and exactly diagonalized. This method is shown to be more accurate than previous truncation methods, while there is no additional computational complexity.

Three-dimensional electron gas with localization along one, two, and three directions

A powerful non-perturbative technique, which allows a direct evaluation of the ground state properties of an interacting electron gas in three dimensions, has been developed. In a unified approach, the low-, intermediate-, and high-density regions are considered. This technique is applied to three-dimensional (3D) systems with periodic electron density along one and two directions. The electronic and magnetic states of these systems are theoretically studied on the basis of the deformable jellium model, within a self-consistent Hartree–Fock approach. To determine the magnetic character of the 3D electron gas ground state, the paramagnetic and ferromagnetic energies are calculated and compared at low, intermediate, and high densities. As r s increases, several symmetry and/or magnetic transitions occur, in each system. The electronic and magnetic states obtained are compared with other theoretical results reported in the literature with different models. In addition to planar and linear periodic electron densities, cubic electron densities are considered in order to look for symmetry transitions among these systems.

Unrestricted Hartree-Fock approximation of the extended emery model

We use an unrestricted self-consistent Hartree-Fock approach to calculate the nature of doping states in the three-band Hubbard model. It turns out that for physically relevant parameter values one hole is localized within a small spin-polarized region where five Cu spins are aligned in the same direction. The spin polarization and binding energy between these spinpolaronic states are investigated as a function of different parameters including a Holstein-type electron-phonon coupling on the Cu sites. At higher doping concentration we observe the occurrence of afmon states where the holes are localized in a ring-shaped area. Inside this ring the antiferromagnetic order parameter has inverse sign with respect to the residual antifer-romagnetically ordered plane.

Magnetic character of the deformable jellium.

Ground-state properties for the electron gas, in the deformable jellium, are obtained. Periodic expansions for the state function, with fermion density centered around a cubic lattice, are introduced. The paramagnetic and ferromagnetic ground-state energies are calculated and compared at each density to determine the magnetic character of the deformable jellium. More than one transition point between different magnetic phases are obtained and compared with those reported in the literature with different models. A paramagnetic region at intermediate densities, in the self-consistent Hartree-Fock approach, is recovered. At these densities a symmetry transitions from homogeneous to localized solutions is obtained for both magnetic phases, and at lower densities the electrons are localized into a paramagnetic or ferromagnetic Wigner-like crystal, respectively. \textcopyright{} 1996 The American Physical Society.

Theory of local magnetic anisotropy in amorphous alloys

The local magnetic anisotropy in amorphous transition metal alloys caused by local spin-orbit coupling has been studied by a perturbation treatment on the basis of a semi-empirical self-consistent Hartree-Fock approach for 55 different amorphous iron clusters (12-14 atoms). The corresponding structural units have been selected from a large amorphous model structure (2048 atoms). The numerical approach leads to a random distribution of the local easy directions and local anisotropy energies. The latter are of the same order of magnitude as those of uniaxial crystalline ferromagnets. The present theory is compared with the point-charge model of Cochrane et al. (1974), for the local anisotropy in amorphous alloys containing rare-earth atoms.

Energetics of Al13, Cu13and Ni13clusters of various symmetries

The stability of Al13, Cu13 and Ni13 clusters of various symmetries has been studied by a semi-empirical self-consistent Hartree-Fock approach based on an INDO-type (intermediate neglect of differential overlap) Hamiltonian. The authors have compared FCC, HCP, and icosahedral structures as well as an amorphous model. The calculated energy minimum always corresponds to the icosahedral arrangement.