Alloy analogy of the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation. In the strong coupling limit, a ferromagnetic instability occurs when 1 < N < 2 and 2 < N < 3. We compare this approximation with other approximations and with the exact results.     

Long-range orders in the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation corrected by Lacroix-Lyon-Caen and Cyrot. The static susceptibility method is used. In the strong scattering limit, a ferromagnetic instability for 1 < N < 2 and 2 < N < 3 is confirmed. It is proved that there is no antiferromagnetic or charge-order instability for any N.     

Thermodynamic properties of a two-site Hubbard model with orbital degeneracy

Exact numerical solutions are obtained for a two-site doubly degenerate Hubbard model with 2, 3 or 4 electrons to study the effect of intra-atomic exchange interaction on the ground state and the thermodynamic properties. Some properties of macroscopic systems are reproduced qualitatively. The condition of having the Hamiltonian rotationally invariant in spin space gets important with increasing electron density.     

Slave-Boson Mean-Field Theory of Spin- and Orbital- Ordered States in the Degenerate Hubbard Model

The mean-field theory with the use of the slave-boson functional method has been generalized to take account of the spin- and/or orbital-ordered state in the doubly degenerate Hubbard model. Numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree–Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the antiferromagnetic orbital state is shown to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is negative.     

A doubly degenerate Hubbard model in the strongly correlated limit

Using a doubly degenerate Hubbard model we derive an effective Hamiltonian in the limiting case where the Coulomb repulsion is much greater than the hopping constant. A brief discussion of this Hamiltonian is given.     

Ferromagnetism in the degenerate Hubbard model

We study the ground state of the doubly degenerate Hubbard model in the strong coupling limit. For this limit, we obtain new exact results: when there are N ? 1 electrons, the ground state is ferromagnetic and there is a ferromagnetic orbital ordering; when the number of electrons is between N and 2N, the ground state is also ferromagnetic due to the intra-atomic Hund's coupling. For this second case, we give an estimate of the Curie temperature.     

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory

The Bethe ansatz local density approximation (LDA) to lattice density functional theory (LDFT) for the one-dimensional repulsive Hubbard model is extended to current-LDFT (CLDFT). The transport properties of mesoscopic Hubbard rings threaded by a magnetic flux are then systematically investigated by this scheme. In particular we present calculations of ground state energies, persistent currents and Drude weights for both a repulsive homogeneous and a single impurity Hubbard model. Our results for the ground state energies in the metallic phase compare favorably well with those obtained with numerically accurate many-body techniques. Also the dependence of the persistent currents on the Coulomb and the impurity interaction strength, and on the ring size are all well captured by LDA-CLDFT. Our study demonstrates the value of CLDFT in describing the transport properties of one-dimensional correlated electron systems. As its computational overheads are rather modest, we propose this method as a tool for studying problems where both disorder and interaction are present.     

On the onset of antiferromagnetism in the Hubbard model

It is proved that there is no antiferromagnetic solution to the Hubbard model for a half-filled band, within the alloy analogy and the coherent potential approximation.     

Density functional study of ferromagnetism in alkali metal thin films

Electronic and magnetic structures of (1 0 0) films of K and Cs, having thicknesses of one to seven layers, are calculated within the plane-wave projector augmented wave (PAW) formalism of the density functional theory (DFT), using both local spin density approximation (LSDA) and the PW91 generalized gradient approximation (GGA). Only a six-layer Cs film is found to have a ferromagnetic (FM) state which is degenerate with a paramagnetic (PM) state within the accuracy of these calculations. These results are compared with those obtained from calculations on a finite-thickness uniform jellium model (UJM), and it is argued that within LSDA or GGA, alkali metal thin films cannot be claimed to have an FM ground state. Relevance of these results to the experiments on transition metal-doped alkali metal thin films and bulk hosts are also discussed.     

Correlation effects on the elastic constant and structural transitions associated with degenerate electronic bands

Starting from an analytical expression for the density of states of an s-type band with arbitry Coulomb correlation obtained from a solution of the Hubbard Hamiltonian, an expression for the electronic contribution to the static elastic constant in a narrow doubly degenerate band is derived both in the absence and in the presence of a magnetic field and its dependence on temperature, filling of the band and correlation strengths is studied. Effects of electronic correlation on the temperature of structural transition from cubic to tetragonal phase is evalued.     

Pressure induced valence transitions in the Anderson lattice model

We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V, t, E_f, and U.     

The effective spin hamiltonian and phase separation instability of the almost half-filled hubbard model and the narrow-band s-ƒ model

The effective spin Hamiltonian is constructed in the framework of the almost half-filled Hubbard model on the Cayley tree by means of functional integral technique with the use of static approximation. The system in the ground state appears to be consisting of the ferromagnetic metallic domains and the antiferromagnetic insulating one sprovided that the concentration of excess electrons (or holes) does not exceed some critical value. The connection between the Hubbard model and the s-? model is stated.     

Magnetic ground state of coupled edge-sharing CuO2 spin chains

By means of density functional theory, we investigate the magnetic ground state of edge-sharing CuO2 spin chains, as found in the (La,Ca,Sr)14Cu24O41 system, for instance. Our data rely on spin-polarized electronic structure calculations including on-site interaction [local density approximation plus the multiorbital mean-field Hubbard model (LDA+U)] and an effective model for the interchain coupling. Strong doping dependence of the magnetic order is characteristic for edge-sharing CuO2 spin chains. We determine the ground state magnetic structure as function of the spin-chain filling and quantify the competing exchange interactions.     

Electron Correlations,Spin-Orbit Coupling,and Antiferromagnetic Anisotropy in Layered Perovskite Iridates Sr_2IrO_4

The effects of electron correlations and spin-orbit coupling on the magnetic anisotropy in the antiferromagnetically ordered 5 d perovskite iridates Sr_2IrO_4 is investigated theoretically using a microscopic model includes a realistic five-orbital tight-binding Hamiltonian, atomic spin-orbit coupling, and multi-orbital Hubbard interactions. Hartree-Fock approximation is applied to obtain the ground state properties with varying spin-orbit coupling and electron correlations.We demonstrate that the interplay between the atomic intraorbital Coulomb repulsion and the Hund's rule coupling leads to a remarkable variability of the resulting magnetic anisotropy at a constant nonzero spin-orbit coupling. At the same time, the preferred direction of the ordered antiferromagnetical moment remains unaltered upon changes in the strength of spin-orbit coupling.     

Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.     

Electron Correlations,Spin-Orbit Coupling,and Antiferromagnetic Anisotropy in Layered Perovskite Iridates Sr2IrO4

The effects of electron correlations and spin-orbit coupling on the magnetic anisotropy in the antiferromagnetically ordered 5d perovskite iridates Sr₂IrO₄ is investigated theoretically using a microscopic model includes a realistic five-orbital tight-binding Hamiltonian, atomic spin-orbit coupling, and multi-orbital Hubbard interactions. Hartree-Fock approximation is applied to obtain the ground state properties with varying spin-orbit coupling and electron correlations. We demonstrate that the interplay between the atomic intraorbital Coulomb repulsion and the Hund's rule coupling leads to a remarkable variability of the resulting magnetic anisotropy at a constant nonzero spin-orbit coupling. At the same time, the preferred direction of the ordered antiferromagnetical moment remains unaltered upon changes in the strength of spin-orbit coupling.     

Many-body theory of magnetization of Bloch electrons in the presence of spin-orbit interactions

We derive a theory of magnetization of an interacting electron system in the presence of a periodic potential, spin-orbit interaction and an applied magnetic field in the paramagnetic limits. Starting from a thermodynamic potential, which includes both the quasi-particle and correlation contributions, we show that modifications brought about by the electron-electron interactions for the magnetization in the quasi-particle approximation is precisely cancelled by the contributions due to electron correlations.This is in contrast to the explicit many-body effects seen in case of the magnetic susceptibility and the Knight-shift. The magnetization is expressed as a product of the spin-density and the effective g-factor, mainly due to the spin-orbit interaction. We show the importance of self-energy corrections on the single-particle energy spectrum by considering a variant of the Hubbard Hamiltonian in momentum space.     

Magnetic phases of the Hubbard model

Employing the self consistent binary alloy approximation we obtain the ground state of the Hubbard model for various values of the electron concentration and the Coulomb repulsion U.