We consider projected wave functions for the two-dimensional t-J model. For various wave functions, including correlated Fermi-liquid and Luttinger-type wave functions, we present the static charge-charge and spin-spin structure factors. Comparisons with recent results from a high-temperature expansion by Putikka et al. indicates spin-charge separation at small length scales.

In this paper, we study the localization properties of the wave function of a one-dimensional tight-binding electron moving in an asymptotic periodic potential, ${\mathit{V}}_{\mathit{n}}$=λ cos(2πQn+πα${\mathit{n}}^{\nu }$), where n is the site index and 0<ν<1. For Q rational, the electronic energy band consists of many subbands, and the number of subbands is determined by Q. For λ<2, there are two mobility edges where the eigenstates at the subband center are all extended, whereas the subband-edge states are all localized in every subband. We develop some heuristic arguments to calculate exactly the mobility edges for this model and carry out numerical work to study the localization properties of the model. Our theoretical results are essentially in exact agreement with the numerical results. We calculate the critical exponents δ and β at mobility edges. We also study the nature of the localized, extended eigenstates and mobility edges of this system as a function of λ, α, and ν.

In this paper we give a description of the doping dependence of the $\mathrm{Ni} 2p$ x-ray-absorption spectra of $M_x{\mathrm{Ni}}_{1-x}\mathrm{O}$ ($M=\mathrm{L}\mathrm{i},\mathrm{N}\mathrm{a}$). We will show that a description beyond an atomic-multiplet calculation is required. To study intermediate doping levels use will be made of a two-metal-site cluster, where one side functions as a hole reservoir. From this study it follows that holes are most likely on the oxygen atoms of the ${\mathrm{NiO}}_6$ units around the Li impurities.

The effects of nonmagnetic impurities (Kondo holes) in Kondo insulators (KI’s) are studied based on the U=∞ Anderson model in the framework of a slave-boson mean-field theory under the coherent-potential approximation (CPA). The density of states for f electrons and its variation with the concentration of Kondo holes are calculated self-consistently. The specific-heat coefficient, residual resistivity, and the T=0 static susceptibility in the alloying system are obtained. The results show that the insulating gap in KI’s can be easily smeared out by Kondo holes, and the system changes gradually from an insulator to a heavy-fermion metal with increasing concentration, which is in qualitative agreement with experiments. Furthermore, the appearance of an impurity band in the gap comes out naturally in the dilute limit of our CPA calculations.

The 4f electronic state and the decay process of the photoexcited 4${\mathit{d}}^9$4${\mathit{f}}^{\mathit{n}+1\mathrm{}}$ states in ${\mathrm{CeO}}_2$ are investigated by means of a resonant photoemission technique in the Ce 4d→4f photoabsorption region. Resonant enhancement of the valence-band emission is clearly observed in the giant-absorption region. This confirms the existence of the 4f electron in the ground state of ${\mathrm{CeO}}_2$. The 4f-derived emission exhibits a single-peak distribution rather than a double-peak structure such as observed in other Ce compounds. The Ce 5p emission band, which spreads over about 10 eV and consists of at least three or more fine structures, also shows the resonant enhancement in the giant-absorption region. In the prethreshold region, the Ce 5p fine structures as well as the 4f emission band show enhancements, but these constant-initial-state spectra are different from each other. The obtained results are discussed in terms of the mixed valence in the ground state of ${\mathrm{CeO}}_2$ and of possible intermediate configurations in the resonant photoemission process.

High-resolution Kα x-ray fluorescence spectra of FeO, ${\mathrm{Fe}}_2$${\mathrm{O}}_3$, ${\mathrm{Fe}}_3$${\mathrm{O}}_4$, ${\mathrm{K}}_3$[Fe(CN${)}_6$]⋅${3\mathrm{H}}_2$O, ${\mathrm{K}}_4$[Fe(CN${)}_6$], and Fe (metal) are measured. It is found that the linewidth of Fe K${\mathrm{\alpha }}_1$ (K-${\mathit{L}}_3$) does not follow Van Vleck’s theorem for oxides, but it follows Van Vleck’s theorem for cyanides; the line shapes of FeO, ${\mathrm{Fe}}_2$${\mathrm{O}}_3$, and ${\mathrm{Fe}}_3$${\mathrm{O}}_4$ are nearly identical. These results are rationalized by the spin-unrestricted DV-Xα molecular-orbital calculations of model clusters. The model clusters we tried are [${\mathrm{FeO}}_6$${]}^{10\mathrm{-}}$, [${\mathrm{FeO}}_6$${]}^{9\mathrm{-}}$, [Fe(CN${)}_6$${]}^{3\mathrm{-}}$, and [Fe(CN${)}_6$${]}^{4\mathrm{-}}$ as model clusters of FeO, ${\mathrm{Fe}}_2$${\mathrm{O}}_3$, ${\mathrm{K}}_3$[Fe(CN${)}_6$]⋅${3\mathrm{H}}_2$O, and ${\mathrm{K}}_4$[Fe(CN${)}_6$], respectively. The electronic structures of these clusters are calculated for their ground states and 1${\mathit{s}}^{\mathrm{-}1}$ hole states. It is concluded from these calculations that the charge-transfer effect induced by the creation of the 1${\mathit{s}}^{\mathrm{-}1}$ core hole, which is the initial state of the Kα x-ray emission, reduces the effective number of 3d unpaired electrons of iron oxides, resulting in the K${\mathrm{\alpha }}_1$ width being reduced from that expected from Van Vleck’s theorem. On the other hand, the effective number of 3d unpaired electrons of cyanides in the ground state is conserved in the 1${\mathit{s}}^{\mathrm{-}1}$ core-hole state. Thus Van Vleck’s theorem holds for cyanides.

We present a prescription for performing electronic-structure calculations without the explicit use of a basis. Our prescription combines a higher-order finite-difference method with ab initio pseudopotentials. In contrast to methods that combine a plane-wave basis with pseudopotentials, our calculations are performed completely in real space. No artifacts such as supercell geometries need be introduced for localized systems. Although this approach is easier to implement than one that employs a plane-wave basis, no loss of accuracy occurs. We apply this method to calculate the structural and electronic properties of several diatomic molecules: ${\mathrm{Si}}_2$, ${\mathrm{C}}_2$, ${\mathrm{O}}_2$, and CO.

We have exploited a variety of techniques to study the universality and stability of the scaling properties of Harper’s equation, the equation for a particle moving on a tight-binding square lattice in the presence of a gauge field, when coupling to next-nearest sites is added. We find, from numerical and analytical studies, that the scaling behavior of the total width of the spectrum and the multifractal nature of the spectrum are unchanged, provided the next-nearest-neighbor coupling terms are below a certain threshold value. The full square symmetry of the Hamiltonian is not required for criticality, but the square diagonals should remain as reflection lines. A bicritical line is found at the boundary between the region in which the nearest-neighbor terms dominate and the region in which the next-nearest-neighbor terms dominate. On the bicritical line a different critical exponent for the width of the spectrum and different multifractal behavior are found. In the region in which the next-nearest-neighbor terms dominate, the behavior is still critical if the Hamiltonian is invariant under reflection in the directions parallel to the sides of the square, but a new length scale enters, and the behavior is no longer universal but shows strongly oscillatory behavior. For a flux per unit cell equal to 1/q the measure of the spectrum is proportional to 1/q in this region, but if it is a ratio of Fibonacci numbers the measure decreases with a rather higher inverse power of the denominator.

Ground-state properties of the asymmetric Hubbard model are studied on one-dimensional clusters (rings) with N=6, 8, and 10 sites. The ground-state energy, correlation functions, and phase diagrams are determined for various sets of model parameters. Computations are performed both by exact diagonalization (for N=6) and by an approximate method by which correlation effects can be examined on larger clusters than exact diagonalization allows. In the limiting cases (one limit corresponds to the spinless Falicov-Kimball model and the other to the Hubbard model) our results agree quite well with those obtained analytically for infinite systems.

We have calculated a random-phase-approximation-type expression for the dielectric response function of several large-band-gap insulators using a development of the model suggested by Fry. This model should be good for systems with well-localized valence-electron functions and flat valence-electron bands. We show that in this model it is a minor approximation to use spherically symmetric bands in the integration over reciprocal space. This allows simple and fast evaluations of our expressions, thus avoiding Brillouin-zone integrations and summations over band indices. The results of our calculations are compared with ab initio data on static dielectric matrices from Baldereschi, with model calculations on the static dielectric function from Rezvani and Friauf and with electron-energy-loss spectra for LiF from Fields et al., using only one fit parameter. In addition, the Johnson f-sum rule is tested for this model. We also verify that our approximation gives the correct singular behavior of the (0,K) matrix elements.

We have investigated the effect of pressure on the optical reflectivity (0.5–4 eV, T=300 K) and Raman spectra (T=20–300 K) of ${\mathrm{Sr}}_2$${\mathrm{FeO}}_4$, an insulating compound with iron in the high oxidation state +4. The lowest optical transition near 1.2 eV shifts to lower energy with increasing pressure, and the overall near-infrared oscillator strength starts to increase significantly for pressures above 6 GPa. This behavior is interpreted in terms of a gap narrowing between a local ${}_{}{}^5{}_{}{}^{}$${\mathit{E}}_{\mathit{g}}$ ground state and a ${\mathit{d}}^5$${\mathit{L}}^{\mathrm{-}1}$-like continuum possibly followed by an insulator-metal transition. In addition to the phonon Raman modes, which are allowed in the ${\mathrm{K}}_2$${\mathrm{NiF}}_4$-type crystal structure, we observe a broad Raman band near 350 ${\mathrm{cm}}^{\mathrm{-}1}$. This band develops into a sharp feature upon cooling to 20 K and vanishes in a narrow pressure range around 5.5 GPa. Oxygen isotope substitution experiments prove that the band is related to oxygen vibrations. We consider explanations where the 350 ${\mathrm{cm}}^{\mathrm{-}1}$ mode arises from spin-induced phonon scattering or from small structural displacements of Fe ions.

We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane’s statistical interaction is derived from an exact solution for each of the two models. In the case of the Hubbard chain, the charge (holon) and the spin (spinon) excitations decouple completely and are shown to behave statistically as fermions and bosons, respectively. In both cases the statistical interaction must contain several components; a rule for the particles with the internal symmetry.

We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.

We propose a quantitative estimate of the charge gap that opens in the one-dimensional dimerized Hubbard model at quarter-filling due to dimerization, which makes the system effectively half-filled, and to repulsion, which induces umklapp scattering processes. Our estimate is expected to be valid for any value of the repulsion and of the parameter describing the dimerization. It is based on analytical results obtained in various limits (weak coupling, strong coupling, large dimerization) and on numerical results obtained by exact diagonalization of small clusters. We consider two models of dimerization: alternating hopping integrals and alternating on-site energies. The former should be appropriate for the Bechgaard salts, the latter for compounds where the stacks are made of alternating TMTSF and TMTTF molecules.

Electronic states near a square Fermi surface are mapped onto quantum chains. Using boson-fermion duality on the chains, the bosonic part of the interaction is isolated and diagonalized. These interactions destroy Fermi-liquid behavior. Nonboson interactions are also generated by this mapping, and give rise to an alternate perturbation theory about the boson problem. A case with strong repulsions between parallel faces is studied and solved. This solution discards irrelevant operators in a new interaction Hamiltonian. There is spin-charge separation and the square Fermi surface remains square under doping. At half-filling, there is a charge gap and insulating behavior together with gapless spin excitations. This mapping appears to be a general tool for understanding the properties of interacting electrons on a square Fermi surface.

We have calculated the electronic structures of the valence bands in a series of α-phase (disordered fcc) Ag-Mg alloys over the range 0–30 at. % Mg using the Korringa-Kohn-Rostoker method within the coherent potential approximation (KKR-CPA). We find that the variation of the equilibrium lattice constant with composition is in good agreement with experimental measurements. The bandwidth of the Ag-related d states decreases with the addition of Mg although the position of the bottom of the band remains roughly fixed in energy with respect to the Fermi level; an observation that is consistent with photoemission measurements. The electronic spectral densities are very sharply peaked at the Fermi energy with widths that are <1% of the Brillouin zone dimension and so the Fermi surfaces of the alloys are well defined throughout the zone. The radius of the neck at the L point and the belly radii in the ΓX and ΓK direction increases approximately linearly with increasing Mg content. Taking into account some previous work on the origin of the short range order in Ag-rich alloys, we conclude that the local-density approximation KKR-CPA method provides a realistic description of the electronic structure in α-phase Ag-Mg alloys.

We develop the method of statistical moments for polarized spectra. In addition to the total intensity measured by sum rules, the average transition energy can be studied. A general procedure is given to remove core-level excitations from the spectrum operator and to obtain purely ground-state properties. The potential of the methods is shown by a rederivation of the x-ray-absorption sum rules and branching-ratio rules for the isotropic spectrum and linear and circular dichroism. Insight is obtained into the origins of changes in the first moment of the isotropic spectrum. They measure short-range correlation functions of crystal and exchange fields.

Sum-rule-type results are derived to obtain orbital and spin magnetic moments from polarized core-level photoemission. The spin and orbital moments can be obtained from the first statistical moment of the spin spectrum and the circular dichroism, respectively. Analogous rules apply to all fundamental spectra. A simple diagram is given that shows what information is contained in the higher statistical moments. The core-valence exchange interactions are much simplified by rewriting them as couplings between the orbital moments and spins of the two shells. This allows, at the same time, a more precise treatment of intra-atomic coupling of magnetic moments. Valence-band photoemission is treated as a particle-hole analogue of x-ray absorption. The difference is the absence of a core hole with its interactions. The method of moments can be applied to both many-electron and one-electron theory, and illustrations are given for 3d and 4f systems.

The absorption threshold singularity induced by the conduction-electron–deep-hole final-state interaction is recovered from the Fermi golden rule using a simple second-order perturbation theory. This approach allows a direct physical understanding of the various contributions to the power-law critical exponent. We use this approach to get the absorption singularities for a nonequilibrium Fermi sea (${\mathrm{\mu }}_1$,${\mathrm{\mu }}_2$) instead of (0,μ). We find a diverging behavior at ${\mathrm{\mu }}_2$ and a converging singularity at ${\mathrm{\mu }}_1$. Unexpectedly, the critical exponents of these singularities disobey Hopfield’s well accepted rule of thumb.