Using arguments from two-dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density-correlation function for coupling l and 1/l, where l is an integer. We present overwhelming evidence that the conjecture is indeed correct.

The dynamics of commensurate chromium alloys are produced by the fluctuations of a spin-density wave consisting of bound electron-hole pairs. For a commensurate alloy at any temperature, we find a transverse spin-wave (SW) mode with frequency ω=cq and a longitudinal amplitude mode with dispersion ω=2√${\mathrm{\Delta }}^2$+(cq${)}^2$/4, where c=${\mathit{v}}_{\mathit{F}}$/√3 is the SW mode velocity and 2Δ is the energy required to break apart an electron-hole pair. Unlike in an itinerant ferromagnet, the SW and amplitude modes never intersect. Other fluctuations below the SW mode and above the amplitude mode are intrinsically damped in an itinerant antiferromagnet.

A Mori-Lee theoretic study of spin relaxation in the neighborhood of a magnetic impurity in the s=1/2 nearest-neighbor (NN) Heisenberg chain at high temperatures is presented. Our calculations suggest that in the limit of zero impurity coupling, the spectral function for the ‘‘surface spin’’ is consistent with a set of discrete frequencies given approximately by ${\mathit{w}}_{\mathit{n}}$≊[n(${\mathit{w}}_0$+1/4)-1/4] against a shallow continuum background, where ${\mathit{w}}_0$≊3J/4 with 2J being the coupling between NN spins. The frequencies broaden as the impurity coupling is increased to the NN coupling.

A microscopic calculation of the effective mass of one ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ impurity in homogeneous liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at zero temperature is performed for an extended Jastrow-Slater wave function, including two- and three-body dynamical correlations and also backflow correlations between the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom and the particles in the medium. The effective mass at equilibrium density, m〈main${\mathrm{〉}}_4^{\mathrm{*}}$/${\mathit{m}}_4$=1.21, is in very good agreement with the recent experimental determination by Edwards et al. The three-particle correlations appear to give a small contribution to the effective mass and different approximations for the three-particle distribution function give almost identical results for ${\mathit{m}}_4^{\mathrm{*}}$/${\mathit{m}}_4$.

We report a measurement of the Nernst effect in the normal state of a cuprate superconductor, ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$, over the temperature range from ${\mathit{T}}_{\mathit{c}}$ to above room temperature. The signal is small: the Nernst coefficient, Q, is never larger than 3 nV/K T over the entire temperature range. The negative sign of Q suggests that the cyclotron scattering rate, 1/${\mathrm{\tau }}_{\mathit{H}}$, increases with particle energy in ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$.

We report a series of measurements of I-V curves for a c-axis-oriented ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$/Ag tape immersed in liquid oxygen. By applying the critical scaling analysis to the I-V characteristics measured in various magnetic fields, a vortex-glass–liquid phase-transition line was identified in the mixed state of this system for H≤1.2 T, with critical exponents ν=1.25±0.15 and z=8.5±1.5. We also show that this transition boundary in the H-T plane defines the upper limit of useful current carrying capacities for the ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$/Ag tapes at a given temperature and magnetic field.

The superconducting transition temperatures (${\mathit{T}}_{\mathit{c}}$’s) of optimally doped ${\mathrm{HgBa}}_2$${\mathrm{Ca}}_{\mathit{m}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{m}}$${\mathrm{O}}_{2\mathit{m}+2+\mathrm{\delta }}$ (Hg 1:2:m-1:m) with m=1, 2, and 3 and ${\mathrm{Hg}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{8+\mathrm{\delta }}$ [Hg(xPb) 1:2:2:3] have been investigated resistively under quasihydrostatic pressures up to 45 GPa. There seems to be a universal upward shift of ${\mathit{T}}_{\mathit{c}}$ under pressure, regardless of m, for all Hg 1:2:m-1:m, implying a common origin for all compounds. Record high ${\mathit{T}}_{\mathit{c}}$’s of 164, 154, and 118 K were reached for the optimally doped Hg 1:2:m-1:m with m=3, 2, and 1, respectively. However, the ${\mathit{T}}_{\mathit{c}}$ enhancement is suppressed by Pb substitution, suggesting the possibility that Hg plays an important role in these compounds.

We consider a magnetic impurity which interacts by hybridization with a system of strongly correlated conduction electrons. The latter are described by a Hubbard Hamiltonian. The charge degrees of freedom of the magnetic impurity are eliminated by means of a canonical transformation, which reduces to the Schrieffer-Wolff transformation in the case of uncorrelated conduction electrons. In the limit of strong correlations, the coefficient of the dominant exchange coupling of the magnetic impurity with the nearest lattice site is modified. When the system is hole doped, there is also an antiferromagnetic coupling to the nearest neighbors of that site involving, additionally, a hole. Furthermore, it is found that the magnetic impurity attracts a hole. In the case of electron doping, double occupancies are repelled by the impurity. In contrast to the hole-doped case, we find no magnetic coupling that additionally involves a doubly occupied site.

We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth nonsingular Fermi-liquid interactions we obtain Shankar’s renormalization-group flows to second order in the BCS coupling and reproduce well-known results for quasiparticle lifetimes. We demonstrate by explicit calculation that spin-charge separation does not occur when the Fermi-liquid interactions are regular. We also explore the relationship between quantized bosonic excitations and zero-sound modes and present a concise derivation of both the spin and the charge collective-mode equations. Finally we discuss some aspects of singular Fermi-liquid interactions.

All previous electronic-structure calculations of Gd have obtained a density of states N(${\mathit{E}}_{\mathit{F}}$) much larger than the experimental value. By comparing Hartree-Fock with local-spin-density-approximation (LSDA) atomic calculations we previously concluded that the minority-spin 4f resonance just above ${\mathit{E}}_{\mathit{F}}$ in the metal, which is responsible for the enhanced N(${\mathit{E}}_{\mathit{F}}$), is an artifact of the LSDA. We present here a calculation for the Gd crystal in which the conduction electrons experience a Hartree-Fock potential due to the core electrons and a LSDA potential due to themselves. The resonance is gone, N(${\mathit{E}}_{\mathit{F}}$) is less than the experimental value (many-body effects will increase it), and the lattice constants are in near-perfect agreement with experiment.

This paper reports calculations of the spectral weight for the lattice Anderson model, defined on a square (four-site) cluster, by exact diagonalization. The calculations emphasize the change in the density of states as the interaction strength U varies between weak and strong limits. We consider system parameters and occupancies such that the model resembles either a conventional insulator or a conventional metal for weak interactions. Then increasing interaction strength leads in the first case to a Kondo insulator in which there is a gap at the chemical potential between hole and electron states. In the metallic case, several features of the Kondo effect in bulk systems are observed. We also observe the splitting of the f band, leading to the formation of an upper Hubbard band at high energy with some double-site occupancy, while states with two f holes on a site are also separated to form a satellite.

We develop a technique to determine the occupied eigenstates in the matrix formulation of the electronic-structure problem. The theory uses a random vector projected onto the electron occupied subspace by use of a Fermi-Dirac projection operator. This random starting vector is inserted into the recursion scheme to generate all occupied eigenenergies and eigenvectors of the system. The method produces a tridiagonal Hamiltonian matrix, which unlike the original Hamiltonian matrix, can be diagonalized even for a very large system. Hellmann-Feynman forces are readily obtained because the eigenvectors can be efficiently computed. Care must be taken to correct for instabilities in the three-term recurrence which gives rise to spurious solutions.

The variety and complexity of the metal-insulator transitions that ${\mathrm{V}}_2$${\mathrm{O}}_3$ undergoes, in both pure form and when doped with other transition-metal ions, have resulted in widespread interest in the electronic structure of this oxide. We report here the results of a photoemission study of the electronic structure of Cr-doped ${\mathrm{V}}_2$${\mathrm{O}}_3$ in metallic and insulating states. At room temperature, insulating Cr-doped ${\mathrm{V}}_2$${\mathrm{O}}_3$ exhibits a low emission intensity at ${\mathit{E}}_{\mathit{F}}$. When cooled, a transition to a metallic state is observed at 210 K. The emission intensity at ${\mathit{E}}_{\mathit{F}}$ and the width of the V 3d emission increase below this transition. Additionally, the O 1s and V 2p core-level structure changes, resembling that of the metallic state of pure ${\mathrm{V}}_2$${\mathrm{O}}_3$. When cooled further, another transition occurs from the metallic state to a second insulating state. The emission intensity at ${\mathit{E}}_{\mathit{F}}$ decreases and the V 3d emission narrows. The core-level emission structure reverted to that of the room-temperature insulating state. The changes in density-of-states and bandwidth were found to be consistent with a Fermi-liquid theory of these transitions; the changes in core-level emission are identified with different core-hole screening in the metallic and insulating states.

The properties of the three-dimensional uniform electron gas in the Fermi liquid regime are analyzed using variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo methods. Our study extends those of Ceperley [Phys. Rev. B 18, 3126 (1978)] and Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)] to larger system sizes with improved statistics and, more importantly, to partial spin polarization. The density range 0.8≤${\mathit{r}}_{\mathit{s}}$≤10, which is the most relevant for density functional computations, is studied in detail. We analyze the size dependence of the simulation results and present an extended set of correlation energies extrapolated to the thermodynamic limit. Using the VMC method we analyze the spin dependence of the correlation energy, and we compare our results to several interpolation formulas used in density functional calculations. We summarize our results by a simple interpolation formula. In addition, we present results for the radial distribution function, the structure factor, the momentum distribution, and triplet correlation functions, and we discuss the comparison with many-body semianalytic theories.

Reflectivity spectra of trivalent rare-earth hexaborides (R${\mathrm{B}}_6$; R=La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, and Y) and mixed-valent ${\mathrm{SmB}}_6$ have been measured in the photon energy region from 1 meV to 40 eV at 300 and 9 K. We discuss the absorption structure due to conduction electrons. Even in ${\mathrm{LaB}}_6$ and ${\mathrm{YB}}_6$, which have no 4f electrons, the optical conductivity spectra were not fitted by a simple Drude model and a frequency-dependent relaxation time was observed. This was attributed to the electron-phonon and electron-electron scattering. In R${\mathrm{B}}_6$ with 4f electrons, a common absorption structure was observed at the energy position of about 0.6 eV. The intensity was found to be almost proportional to the 4f spin angular momentum. From the f-sum rule, the absorption was found to be due to the conduction electrons. The origin was assigned to be due to the transition or to the relevant exciton absorption from the saddle points of ${\mathrm{\Sigma }}_1$ at the neck point to the saddle points of ${\mathrm{\Gamma }}_{12}$ and ${\mathrm{\Gamma }}_{25}$ assisted by the scattering of the intra-atomic 5d-4f Coulomb exchange interaction, in particular enhanced in the heavy R${\mathrm{B}}_6$ compounds by the lattice instability. In ${\mathrm{SmB}}_6$, the absorption that was seen in trivalent R${\mathrm{B}}_6$’s was also observed in addition to absorptions from 4f states of ${\mathrm{Sm}}^{2+}$ to 5d states and from 5d to 4f in ${\mathrm{Sm}}^{3+}$. This is thought to mean that the Fermi level of ${\mathrm{SmB}}_6$ is located at the same energy position in the band structure as that of the trivalent R${\mathrm{B}}_6$.

Conditions for Anderson localization are derived for three cases: (1) anisotropic three-dimensional metal, (2) quasi-two-dimensional metal, and (3) quasi-one-dimensional metal. For all these cases the conductivity at T=0 as well as the interference correction are calculated. The simplest models are used. From the estimate Δσ/σ∼1, localization conditions are obtained. It is shown that localization takes place in all three cases but in cases (2) and (3) the critical value of the random potential is essentially reduced if the overlap integrals are small. In a two-dimensional metal this refers to the conductivity along the planes whereas for the conductivity perpendicular to the planes the three-dimensional condition applies, i.e., contrary to common wisdom localization in this direction is more difficult to reach than along the planes.

The spectrum of Harper’s equation (a model for Bloch electrons in a magnetic field) is a fractal Cantor set if the ratio β of the area of a unit cell to that of a flux quantum is not a rational number. It has been conjectured that the second moment of an initially localized wave packet has a power-law growth of the form 〈${\mathit{x}}^2$〉∼${\mathit{t}}_0^{2\mathit{D}}$, where ${\mathit{D}}_0$ is the box-counting dimension of the spectrum, and that ${\mathit{D}}_0$=1/2. We present numerical results on the dimension of the spectrum and the spread of a wave packet indicating that these relationships are at best approximate. We also present heuristic arguments suggesting that there should be no general relationships between the dimension and the spread of a wave packet.

The behavior of strongly correlated electrons in disordered systems is investigated using a functional integral formulation of the problem. In the mean-field approximation, which becomes exact in the limit of large spatial dimensionality, the problem reduces to the solution of an ensemble of self-consistently determined Anderson impurity models. The methods are applied to different classes of disorder, and the possible phases of the system are analyzed. We present results for the behavior of the thermodynamic and transport properties near the metal-insulator transitions for each case considered. When strong hopping disorder is present, disorder-induced local-moment formation is found, leading to qualitative modifications of metallic phases even away from the transition. Finally, we indicate how our approach can be systematically extended beyond the mean-field limit, where the presence of spatial fluctuations makes it possible to address the problem of Anderson localization in strongly correlated electronic systems.

Using a mean-field statistical description, we derive a general formalism to investigate atomic short-range order in alloys based on a density-functional description of the finite-temperature, grand potential of the random alloy. This ‘‘first-principles,’’ Landau-type approach attempts to treat several contributions (electronic structure, Fermi surface, electrostatics, magnetism, etc.) to the electronic energy on an equal footing. An important ingredient for the statistical averaging is the replacement of the molecular mean fields (Weiss fields) with Onsager cavity fields, which forces the diagonal part of the fluctuation-dissipation theorem to be obeyed. To show its general applicability and usefulness, we apply the theory to three fcc alloy systems. In ${\mathrm{Cu}}_{0.75}$${\mathrm{Pd}}_{0.25}$, the incommensurate atomic short-range order is driven by a Fermi-surface effect, in agreement with earlier work. In contrast, ${\mathrm{Pd}}_{0.5}$${\mathrm{Rh}}_{0.5}$ exhibits clustering tendencies, with both band-filling and charge-rearrangement effects being important in setting the spinodal temperature at 1150 K, in good agreement with experiment. In the final examples of three nickel-rich NiCr alloys, previously ignored electrostatic effects are found to play a significant role in determining the atomic short-range order.

We use a ‘‘first-principles’’ concentration-wave approach based on a finite-temperature, electronic density-functional, mean-field, grand potential of the random alloy to investigate the high-temperature atomic short-range order (ASRO) in ${\mathrm{Ni}}_{75}$${\mathrm{V}}_{25}$ and ${\mathrm{Pd}}_{75}$${\mathrm{V}}_{25}$ solid solutions. Experimentally, these similar alloys both develop D$0_{22}$-type long-range order at low temperatures but different ASRO at high temperatures. Our calculations describe the measured ASRO well. We compare these results with those found for a hypothetical ${\mathrm{Co}}_{75}$${\mathrm{Ti}}_{25}$ solid solution. Since this alloy orders directly from the melt into the L$1_2$ phase, it should exhibit strong L$1_2$-like ASRO, as we find in our calculations. We analyze the features in the calculated diffuse intensities in terms of various factors in each alloy’s electronic structure. Because we have assumed that the atoms are fixed to the Bravais lattice, we discuss two additional examples, ${\mathrm{Al}}_{75}$${\mathrm{Ti}}_{25}$ and ${\mathrm{Ni}}_{50}$${\mathrm{Pt}}_{50}$, to show the limitations of neglecting atomic displacements. Notably, the Onsager cavity fields have been incorporated into the theory to conserve the diffuse scattering intensity over the Brillouin zone and to provide a better description of the long-ranged, electrostatic screening effects.