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While Anderson (1992) states that his theory of high-temperature conductivity is consistent with many experimental constraints, most (and perhaps all) of his observations and explanations have been produced after obtaining experimental results. It is suggested that he describe an experimental test that might prove his theory wrong. Anderson replies that the predictive power of his theory is attested by three notable post-theory confirmations, and notes that the theory has passed all experimental tests to date. 4 refs.

We discuss the properties of spin-wave theory of quantum antiferromagnets with an additional constraint that restores the sublattice symmetry. Our treatment is analogous to Takahashi's recent theory of low-dimensional ferromagnets, and closely related to the Schwinger boson theory of Arovas and Auerbach. We obtain exact results for spin-spin correlations of 2, 4, and 8 spins in a singlet state, and exceedingly close agreement with exact results for S=(1/2 in a variety of other cases. The implication for the long-range order of the d=2, S=(1/2 Heisenberg antiferromagnet is discussed.

The possibility of superconductivity arising from interactions involving nearest neighbor singlet pairs is discussed. It is shown that the strong coupling effective Hamiltonian for the Hubbard model only admits extended s-wave solutions, and it is argued that those are suppressed by the Hubbard U. Neglecting hopping terms in the effective Hamiltonian involving three sites while keeping nearest neighbor superexchange and/or density interactions introduces spurious d- and p-wave solutions. A related but more fundamental interaction describing covalent bonds between polarizable ions can give rise to extended s-wave superconductivity, and the relationship with the resonating valence bond picture is discussed.

The ground state and gap properties of a spinless model of $f$ and $d$ electrons with hybridization $V$ and $f\ensuremath{-}d$ interaction ${U}_{\mathrm{fd}}$ are studied in one dimension using a real-space renormalizationgroup (RG) method. To understand the dependence of the RG results on the cell size chosen, we first study the problem for ${U}_{\mathrm{fd}}=0$ and arbitrary cell size $N$. It is found that even-site cells give qualitatively incorrect results for the gap, while odd-site cells (as small as $N=3$) reproduce very accurately the exact results for the gap and give a reasonable upper bound for the groundstate energy. On the basis of this result the phase diagram is studied as a function of arbitrary $V$ and ${U}_{\mathrm{fd}}$ using three site cells. We consider the half-filled band situation for which the ground state is found to be insulating for all values of ${U}_{\mathrm{fd}}(\ensuremath{\ne}0)$. The $f$-electron occupation number as a function of ${E}_{f}$ changes continuously, confirming recent mean-field results. This result indicates that the interacting $f\ensuremath{-}d$ system does not scale to a single impurity model as argued in previous studies. Using a Jordan-Wigner transformation from spin to fermion operators, the Kondo necklace model is mapped onto a fluctuating valence model and the transition from ferromagnetic to Kondo-state behavior is numerically studied using $N=3$.

Tone bursts of 500, 1 000, or 3 000 Hz with rise/fall times of 3, 5, and 10 msec were combined with either a 'no plateau' duration or 'equivalent durations' of 10 or 30 msec. Electroencephalic activity (102.4 msec post-stimulus) from normal-hearing adults was recorded between the vertex and each earlobe. AER latencies and amplitudes decreased as frequency increased but effects of increasing rise/fall time and duration were similar at all frequencies. An increase in stimulus rise/fall time or equivalent duration results in increases of about 1-3 msec in latencies of all middle component peaks. Increasing either rise/fall time or equivalent duration produces a considerable reduction in middle component amplitude at all intensity levels. Any combination of rise/fall time and plateau duration that gives an equivalent duration of less than 10 msec. and results in narrow spectra stimuli, appears optimal for clinical EEA with middle components.

We point out that a standard Monte Carlo algorithm can be made to converge in some cases for nonpositive definite weights. Comparison of Monte Carlo and Langevin algorithms for two simple models with complex actions shows the Monte Carlo method to be always superior; it is more reliable and gives smaller statistical error when both converge, and converges in cases where the Langevin method does not.

Monte Carlo simulations are used to study the charge-density-wave to spin-density-wave transition in the one-dimensional Hubbard model with on-site ($U$) and nearest-neighbor ($V$) repulsion. The transition is found to be continuous for small $U$ and first order for large $U$, with the crossover occurring around $U\ensuremath{\sim}3$. The transition line deviates somewhat from the theoretical prediction $U=2V$ towards the charge-density-wave phase for intermediate coupling. A qualitative explanation for the results is given by use of strong-coupling arguments.

We study the properties of an effective Hamiltonian to describe the propagation of holes through the oxygen anion network in a high-${T}_{c}$ superconductor. Approximate parameters for our Hamiltonian are derived from atomic properties of O. The effective interaction between holes and the effective bandwidth for the holes are studied by diagonalization of finite clusters. The effective interaction is found to be attractive for realistic parameters; in the same regime, there is significant band narrowing. Consequences of our results for normal and superconducting properties of high-${T}_{c}$ oxides are discussed.

The real-space dynamic renormalization group method developed in previous papers is applied to the kinetic Ising model defined on a square lattice. In particular we extend the formalism to the calculation of space- and time-dependent equilibrium averaged correlation functions. We find that conventional methods for implementing the real-space renormalization group via cumulant expansions in terms of the intercell coupling lead to correlation functions which decay algebraically in space at large distances in the disordered phase in qualitative disagreement with the known exponential decay. We indicate how one can develop new perturbation theory expansion methods which lead to the proper exponential decay at large distances and also lead to good quantitative results for other observable quantities like the magnetization, susceptibility, and single spin time autocorrelation function. As the result of a first-order calculation we obtain excellent results for the static critical exponents and a value of $z=1.79$ for the dynamic critical exponent. The critical exponents obtained from the correlation functions calculated using this method satisfy the proper static and dynamic scaling relations.

Hydrogen at high densities is expected to undergo a transition from a molecular to a metallic state. It is shown here that in a range of metallic densities hydrogen is likely to possess partial spin polarization, analogously to iron. It is suggested that this is the origin of magnetic fields in planets and stars.

Using fermion Monte Carlo techniques we have studied the properties of a one-dimensional electron-exciton system. The zero frequency wave vector charge-density, spin-density and pairing susceptibilities were evaluated for a variety of band fillings and interaction parameters. We find that retardation and band filling are essential in determining which correlations are dominant at low temperature. While for a single chain it is possible in the strong coupling regime to have pairing correlations diverge more rapidly than charge density wave correlations, we argue that interchain couplings will lead to a 3-D charge density wave phase.

We show that the tendency for superconductivity of a weakly coupled 2D electron system can be significantly enhanced if the Fermi energy is close to a logarithmic Van Hove singularity in the density of states. Using results from perturbation theory, supported by quantum Monte Carlo simulations, we calculate ${T}_{c}$ and explore the effects of the quasiparticle lifetime and higher-order interactions on this enhancement. This mechanism suggests possible new directions in the search for 2D excitonic superconductivity.

Within the conventional electron-phonon mechanism of superconductivity, normal-insulator-superconductor (N-I-S) tunneling characteristics are expected to be symmetric with respect to the sign of the bias voltage. A recently proposed mechanism of superconductivity based on pairing of hole carries predicts an asymmetry of universal sign: the tunneling current should be larger for a negatively biased sample. We suggest a search for this asymmetry in conventional superconductors, as well as in “hole” and “electron” oxide superconductors: its systematic observation would provide direct evidence in favor of the hole pairing mechanism of superconductivity.

We study the nature of the ground state of the Su-Schrieffer-Heeger model for electron-phonon interactions in one dimension in the half-filled-band case. We consider the cases of spinless electrons ($n=1$) and spin-\textonehalf{} electrons ($n=2$), and discuss the stability of the Peierls-dimerized ground state as a function of the ionic mass and electron-phonon coupling constant. We first consider the zero-mass limit of the theory and extend our results to finite mass using renormalization-group arguments. For spinless electrons, it is found that quantum fluctuations destroy the long-range dimerization order for the small electron-phonon coupling constant if the ionic mass is finite. For spin-\textonehalf{} electrons, the system is dimerized for an arbitrary coupling constant and phonon frequency. Renormalization-group trajectories show that the low-energy behavior of the system is governed by the zero-mass limit of the theory, an $n$-component Gross-Neveu model. Monte Carlo simulations are performed for the model at finite phonon frequencies, and the results are compared with the static limit result. We study in particular the set of parameters appropriate for polyacetylene and find a 15% reduction in the phonon order parameter due to fluctuations of the phonon field. A finite-size scaling analysis of the numerical data for the cases $n=1 \mathrm{and} 2$ is performed, which confirms the results obtained from the renormalization-group analysis.

We solve numerically a set of coupled integral equations due to Halperin to obtain the spectral density of a random chain of oscillators. The results are compared with coherent-potential-approximation (CPA) and Monte Carlo calculations. The accuracy of CPA is found to be similar to that achieved in CPA calculations of the density of states: the gross features of $A(q,\ensuremath{\mu})$ are correctly reproduced; the fine structure is averaged out. The agreement between exact and Monte Carlo calculations is excellent.

We discuss a new method to perform numerical simulations of one-dimensional systems with fermion and boson degrees of freedom. The method is based on a direct-space, imaginary-time representation of the fermion field. It is fast so that systems having up to 100 sites can easily be simulated. In addition, the method provides an intuitive physical "picture" of the ground state of a one-dimensional many-body system. We discuss in detail how to implement the method and how to compute various physical quantities. In particular, we show how to extend the method to study averages of off-diagonal quantities in an occupation-number representation. To assess the accuracy of our procedure, we apply it to free fermions in one dimension and compare with exact results. We then study a model of spinless interacting fermions and obtain the expected phase structure and behavior of correlation functions. We also consider the extended Hubbard model at various points in its phase diagram and study the behavior of spin-density, charge-density, and pairing correlation functions. We then study the Gross-Neveu model and show how the behavior depends on the number of fermion flavors. Finally, we consider an electron-phonon model and study its behavior both in the one-particle polaron sector and in the half-filled-band case. Along the way we show pictures of the ground-state configurations that give physical insight into the properties of the systems, like charge-density-wave, spin-density-wave, and superconducting states, "fractional charges," and solitons. We conclude by comparing our method with other methods and discuss the possibility of extending it to higher dimensions.

A two-dimensional model of interacting electrons on a lattice, the Hubbard model, has been studied by means of a numerical simulation technique. Results for the half-filled-band sector are presented for lattices of up to 6\ifmmode\times\else\texttimes\fi{}6 spatial sites, as a function of temperature and electron-electron repulsion $U$. In the ground state, the system is found to exhibit antiferromagnetic long-range order for all values of $U$, although greatly reduced from the mean-field-theory predictions.

A new Monte Carlo approach applicable to systems with fermion and boson degrees of freedom is proposed. The main advantage of the method is its speed: For systems in one space and one time dimension (1 + 1) the calculation reduces to doing Monte Carlo computations on a two-dimensional classical system with local interactions. Here the potential of the method is illustrated by application to various (1 + 1)-dimensional systems.

We review recent work on a mechanism proposed to explain high T c superconductivity in oxides as well as superconductivity of conventional materials. It is based on pairing of hole carriers through their direct Coulomb interaction, and gives rise to superconductivity because of the momentum dependence of the repulsive interaction in the solid state environment. In the regime of parameters appropriate for high T c oxides this mechanism leads to characteristic signatures that should be experimentally verifiable. In the regime of “conventional superconductors” most of these signatures become unobservable, but the characteristic dependence of T c on band filling survives. New features discussed here include the demonstration that superconductivity can result from repulsive interactions even if the gap function does not change sign and the inclusion of a self-energy correction to the hole propagator that reduces the range of band filling where T c is not zero.

Is is proposed that a bond-charge repulsion term that necessarily arises in deriving a tight-binding Hamiltonian from first principles plays a fundamental role in superconductivity. This term is repulsive for bonding states and attractive for antibonding states. Together with the reduction of the local Coulomb repulsion due to atomic polarization this effect can explain the occurence of superconductivity in solids without involving the electron-phonon interaction.

Near nesting of the Fermi surface can lead to low-frequency spin-density, charge-density and lattice modes at wave vectors connecting the nested regions. We find that the exchange of these excitations leads to a superconducting coupling constant for d-wave pairing which is enhanced near the Fermi-surface instability.

The effect of quantum fluctuations of the phonon field on the ground-state character of one-dimensional electron-phonon systems is studied with a numerical simulation technique. Two different electron-phonon models are studied, both for spinless and spin-\textonehalf{} electrons, in the half-filled-band case. In both models, it is found that in the spinless case quantum fluctuations destroy the long-range dimerization order for small electron-phonon coupling constant $\ensuremath{\lambda}$. For the spin-\textonehalf{} case, the results are consistent with the Peierls transition occurring at $\ensuremath{\lambda}=0$.

Using a path-integral formulation for the partition function the two-impurity symmetric Anderson model in the local-moment regime is mapped onto a problem of a classical four-component "Coulomb" gas interacting with a logarithmic potential. This can be viewed alternately as a problem of a general four-state spin system with inverse-square interaction in one dimension. The scaling equations for this model are derived and their implications for the properties of the Anderson model are pointed out. This mapping, although approximate, provides an explicit and physically interesting realization of a class of general $n$-state inverse-square spin systems in one dimension.

We investigate the magnetic properties of the Kondo two-impurity Hamiltonian with a recently introduced, essentially exact quantum Monte Carlo technique. We explore in particular the competition between Kondo effect, with Kondo temperature ${T}_{K}$, and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, with coupling constant scrJ. We simulate the regimes \ensuremath{\Vert}scrJ\ensuremath{\Vert}${T}_{K}$ and \ensuremath{\Vert}scrJ\ensuremath{\Vert}\ensuremath{\gtrsim}${T}_{K}$ for both ferromagnetic and antiferromagnetic scrJ, considering in particular the antiferromagnetic regime scrJ/${T}_{K}$\ensuremath{\approxeq}2.4 where anomalous behavior is predicted from renormalization-group calculations. Over the entire parameter range, we find that nearby impurity spin-spin correlations initially develop according to a RKKY effective Hamiltonian ${H}_{\mathrm{eff}}$=scrJ${\mathrm{S}}_{1}$\ensuremath{\cdot}${\mathrm{S}}_{2}$ as the temperature is lowered; the correlations then saturate at around the Kondo temperature ${T}_{K}$. This result suggests an analogous picture for the lattice case, with long-range order developing if a ``RKKY lattice'' transition temperature is reached before Kondo quenching effects set in. We also find no evidence for anomalous staggered susceptibility behavior in the scrJ/${T}_{K}$\ensuremath{\approxeq}2.4 regime, and give possible explanations for this difference with the renormalization-group results.

Un modele de bande recemment propose pour decrire le ferro-magnetisme metallique est etudie a temperatures finies dans l'approximation du champ moyen. Discussion du comportement de la temperature critique, de la chaleur massique, de la susceptibilite magnetique au-dessus de T c et de l'aimantation en dessous de T c en supposant une densite d'etats constante

Using a recently proposed quantum Monte Carlo technique, we consider moment formation and magnetic properties of the symmetric Anderson-impurity model for a wide range of parameters and temperatures. We parametrize the general behavior, determining the approach towards universality and establishing the range of validity of various approximations.

A striking similarity exists between the dependence of T c on carrier concentration in transition metal alloys and in oxide superconductors. Such a dependence follows naturally from a mechanism of superconductivity based on pairing of hole carriers through Coulomb interactions.

We have studied the tendency of the two-dimensional half-filled Hubbard model towards dimerization as a function of the on-site repulsion U. We have found that the phonon with (\ensuremath{\pi},\ensuremath{\pi}) wave vector is the most favorable vibration mode when U is less than a critical value ${U}_{c}$, where ${U}_{c}$ is a function of the dimerization. When U is greater than ${U}_{c}$, the (\ensuremath{\pi},0) phonon becomes preferred. In leading order, the energy gain under dimerization appears to be proportional to ${\ensuremath{\delta}}^{2}$ln\ensuremath{\delta} if the (\ensuremath{\pi},\ensuremath{\pi}) phonon is favorable, so that the system displays a Peierls instability in this case. For large U the energy gain to leading order appears to be proportional to ${\ensuremath{\delta}}^{2}$ for both the (\ensuremath{\pi},\ensuremath{\pi}) and (\ensuremath{\pi},0) phonons, and the latter one is preferred; in that case the system is stable unless the electron-phonon coupling exceeds a critical value. Unlike the effect in the one-dimensional case, the on-site repulsion U seems to have essentially no effect on the tendency towards dimerization for small U, and suppresses it for large U. This difference may be related to the fact that there exists long-range antiferromagnetic order in the two-dimensional half-filled Hubbard model when U is present.

We discuss Monte Carlo algorithms for fermion lattice systems based on exact updating of the fermion Green's function. A space and a space-time algorithm are shown to be limiting cases of a formulation that smoothly interpolates between them. This new formulation can to a large extent preserve the desirable features of both limits and suppress the undesirable ones.

We discuss results of simulations of the Hubbard model of interacting electrons on a lattice. We start with a brief discussion of methodology and point out some of the outstanding problems. We then discuss results of simulations of the model in three, two, and one dimension, particularly in connection with its magnetic and superconducting properties. We conclude with a brief discussion of future directions.

Various theoretical models have suggested superconductivity induced by an on-site Hubbard repulsion U. Results of numerical calculations on small two-dimensional systems are reviewed, which show that just a Hubbard U can induce antiferromagnetism but not superconductivity. Reasons for the failure of the theoretical models based on pure spin mechanisms are discussed. In contrast, a model with U and a nearest-neighbor repulsion V is shown to exhibit antiferromagnetism and pairing in different regimes, suggesting that this model contains the essential physics of high Tc.

Etude de l'appariement, de la densite de charge et des correlations de densite de spin d'un modele exciton-electron unidimensionnel

We propose a new algorithm to compute dynamic correlation functions in quantum systems at zero temperature using Monte Carlo techniques. The method, which avoids inverse-Laplace transforms, is based on a representation of the Dirac $\ensuremath{\delta}$ function as the limit of a Gaussian. We illustrate the method on the one-dimensional harmonic oscillator.

We show that planar CuO/sub 2/ clusters with strong repulsive Coulomb interactions can exhibit an effective attractive pairing interaction. This interaction arises from a disruption of the local lattice charge distribution produced when a hole is added and occurs for a wide range of parameter values, in the region where both the on-site Cu repulsion and the nearest-neighbor Cu-O repulsion are appreciable. A signature of this mechanism is that the occupation of Cu sites decreases as the system is doped. We suggest that this effective attractive interaction is responsible for high-T/sub c/ superconductivity in oxides

We continue our study of correlation functions in the one-dimensional Hubbard model with the use of a Monte Carlo technique. This paper focuses on the behavior of two different particle-hole susceptibilities: the on-site charge-density response function and the nearest-neighbor charge-transfer response function. Although their behavior is predicted to be similar within weak-coupling renormalization-group theory, we find different behavior with our nonperturbative technique. In particular, the charge-transfer susceptibility shows structure at $2{p}_{F}$ for large Coulomb interactions due to spin-Peierls fluctuations, which is absent in the on-site charge-density response. We also study the effect of varying band filling, by comparing results for the $\frac{1}{4}$- filled band ($\ensuremath{\rho}=0.5$) case and the cases $\ensuremath{\rho}=0.61$ and $\ensuremath{\rho}=1$. We find, for example, that it is possible to have structure in the response function at wave vectors that are not simply related to the Fermi wave vector. We discuss the implications of our results to the interpretation of experimental results in various quasi-one-dimensional charge-transfer compounds.

The properties of a model of electrons interacting through an on-site Hubbard repulsion U, and coupled to intersite lattice vibrations, are discussed. It is argued that the antiferromagnetic singlet pairs induced by U will condense into a superconducting state in the presence of coupling to high-frequency phonons, or, equivalently, that an on-site U strongly enhances the electron-phonon coupling giving rise to superconductivity. It is proposed that this model describes the essential features of the high-${T}_{c}$ oxide superconductors.

We study the nature of the ground state of a one-dimensional electron-phonon model for molecular crystals: The phonons are assumed dispersionless and couple to the local electronic density. We consider the half-filled-band sector and discuss the stability of the Peierls-dimerized ground state as a function of the phonon frequency ($\ensuremath{\omega}$), electron-phonon coupling constant ($\ensuremath{\lambda}$), and number of components of the electron spin ($n$). First, we discuss the properties of the model in the limiting cases of zero frequency and infinite frequency. We then perform a strong coupling expansion which maps the system onto a spinless fermion model with nearest-neighbor repulsion for both spinless and spin-\textonehalf{} electrons, but with different parameters in both cases. Finally, we perform a numerical study of the system using a Monte Carlo technique. We study the behavior of the order parameter and of correlation functions for various points in parameter space. We also perform a finite-size---scaling analysis of the numerical data. The conclusions of our study are the following: For the case of spinless electrons, there exists always a disordered phase for small coupling constant, and the system undergoes an infinite-order transition to a Peierls-dimerized state as the coupling constant increases beyond a critical value. The phase diagram is divided between a disordered and an ordered region by a line that connects the points ($\ensuremath{\omega}=0$, $\ensuremath{\lambda}=0$) and ($\ensuremath{\omega}=\ensuremath{\infty}$, $\ensuremath{\lambda}=\ensuremath{\infty}$). For the case of spin-\textonehalf{} electrons, the system is dimerized for arbitrary $\ensuremath{\lambda}$ and $\ensuremath{\omega}$ except in the limit $\ensuremath{\omega}=\ensuremath{\infty}$.

The nearest-neighbor random-exchange Heisenberg antiferromagnetic Heisenberg chain ($s=\frac{1}{2}$) is studied at low temperatures via an approximate renormalization-group method. This entails renormalization of the random-exchange coupling constant $J$ and of the probability law for $J$. ${P}_{0}(J)$. After $n$ iterations we find that the renormalized probability function ${P}_{n}({J}^{(n)})$, a function of the renormalized coupling ${J}^{(n)}$, develops singular behavior for small ${J}^{(n)}$, independent of the initial form of ${P}_{0}(J)$. This happens both for ${P}_{0}(J)$ that diverge or go to zero as $J\ensuremath{\rightarrow}0$. The singular form of ${P}_{n}({J}^{(n)})$ is such that it leads to a specific heat and susceptibility that behave like $C\ensuremath{\sim}{T}^{1\ensuremath{-}{\ensuremath{\alpha}}_{C}(T)}$ and $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}{\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)}$. ${\ensuremath{\alpha}}_{C}(T)$ and ${\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)$ are exponents weakly dependent on temperature ($T$) that go to one as $T\ensuremath{\rightarrow}0$ and satisfy ${\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)g{\ensuremath{\alpha}}_{C}(T)$, for arbitrary initial probability laws. The classical $n$-vector models, and in particular the classical Heisenberg model are also studied using a renormalization-group approach and it is found that their behavior is different than that of the quantum model: singular behavior in the thermodynamic properties is only obtained if the starting ${P}_{0}(J)$ is singular. An explanation of these results in terms of the scaling theory of localization is suggested. The relevance of our results to the experimental findings on the magnetic properties of tetracyanoquinodimethanide complexes is also discussed.