Charge-charge Correlation Function Research Articles

Large Fermi surface of the one-dimensional Kondo lattice model observed by Friedel oscillations

The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density matrix renormalization group method. We calculate spin excitation gap and Friedel oscillations in finite systems. The finite size corrections of the spin gap and the long-range Friedel oscillations are consistent with a Tomonaga-Luttinger liquid. The Friedel oscillations reflect the charge-charge and spin-spin correlation functions. From the period of the Friedel oscillations, it is concluded that the Fermi surface is large including both the conduction electrons and the localized spins, k F = π(1 + n c)/2 where n c is the density of conduction electrons.

Friedel oscillations in the one-dimensional Kondo lattice model.

The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density-matrix renormalization- group method. We observe charge and spin Friedel oscillations. They reflect the long range charge-charge and spin-spin correlation functions. The observed oscillations are consistent with a Tomonaga-Luttinger liquid. From the period of the oscillations it is concluded that the Fermi surface is large, including both the conduction electrons and the localized spins, $k_F=\pi (1+n_c)/2$, where $n_c$ is the density of conduction electrons.

Statics and dynamics of charge fluctuations in the t-J model.

The equation for the charge vertex $\gamma$ of the $t-J$ model is derived and solved in leading order of an 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on $\gamma$ are then calculated, such as the life time and the transport life time of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on $J$ and are mainly determined by the constraint of having no double occupancies of sites.

Toulouse points and non-Fermi-liquid states in the mixed-valence regime of the generalized Anderson model.

We study the mixed valence regime of a generalized Anderson impurity model using the bosonization approach. This single impurity problem is defined by the $U=\infty$ Anderson model with an additional density-density interaction, as well as an explicit exchange interaction, between the impurity and conduction electrons. We find three points in the interaction parameter space at which all the correlation functions can be calculated explicitly. These points represent the mixed valence counterparts of the ususal Toulouse point for the Kondo problem, and are appropriately named the Toulouse points of the mixed valence problem. Two of the Toulouse points exhibit the strong coupling, Fermi liquid behavior. The third one shows spin-charge separation; here, the spin-spin correlation functions are Fermi-liquid-like, the charge-charge correlation functions and the single particle Green function have non-Fermi-liquid behaviors, and a pairing correlation function is enhanced compared to the Fermi liquid case. This third Toulouse point describes the novel intermediate mixed valence phase we have previously identified. In deriving these results, we emphasize the importance of keeping track of the anticommutation relation between the fermion fields when the bosonization method is applied to quantum impurity problems.

Simulation of Ostwald Ripening in Two Dimensions: Spatial and Nearest Neighbor Correlations

Recent experimental results on late stage coarsening (Ostwald ripening) in two dimensions were reinvestigated by means of numerical simulation using the Cahn-Hilliard equation (model B). We determine the spatial particle-particle and charge-charge correlation functions according to the experimental results of Krichevsky and Stavans. We find that our numerical results correspond well with these experiments. We also investigate particle-particle correlations between nearest neighbors (defined by the Voronoi diagram of particle centroids) following the experiments of Seul, Morgan and Sire and compare our numerical results with their Maximum Entropy model of Ostwald ripening.

Fractional charge and correlation exponents for interacting electrons in one dimension.

Close to the transition between incommensurate conductor and commensurate insulator, charge transport in a system of one-dimensional interacting spin-1/2 fermions moving in a periodic potential is done by solitons (i.e., the few extra particles or holes) having a charge $Q$ which is a fraction of the elementary charge $e$. We show that $Q$ is directly related to the limiting value at commensuration of the exponent ${g}_{c}^{*}$ of the charge-charge correlation function: ${g}_{c}^{*}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(Q/e{)}^{2}$. We give some simple rules for determining both charge and spin correlation exponents and point out their dependence on the parity of the order of the underlying umklapp scattering.

Criticality and phase transitions in ionic fluids

Recent experimental investigations of criticality and phase separation in ionic fluids have revealed behavior of great theoretical interest. In seeking to understand the experiments, some of which appear to exhibit argonlike criticality and some of which exhibit “classical” (mean-field) criticality, a convenient starting point is the restricted primitive model (RPM) of symmetrically charged hard spheres, all of equal diameter σ, each sphere bearing a positive or negative charge of magnitudeq. There is overall charge neutrality, so that the expected number densities of the anions and cations are equal,ρ+=ρ-. Studies of RPM charge-charge and density-density correlation functions indicate that the fluctuation-suppressing mechanism that yields mean-field critical behavior in nonionic systems with long-range interparticle potentials is not operative in the RPM. On the basis of plausible assumptions, Ising-like behavior is instead expected. The above work is summarized. New work of Zhang and the author is outlined, showing that when one loses the RPM symmetry (through, e.g., different valence, diameter, or dipole moment of anions and cations) a strong coupling between charge-charge and density-density correlation ensues. The way in which this can be expected to give rise to mean-field or mean-field-like behavior is noted. Other new observations concern the mean-field analogy found by Hoye and the author between the parameter 2/(d−2) (d is the dimensionality) in that model and the monomer number in high polymers, with respect to the coexistence-curve shape dependence on those parameters.

Exact diagonalization study of spin and charge dynamics in the t- J model

We investigate the dynamical spin-spin and charge-charge correlation functions, S( Q ,ω) and N( Q ,ω) , for the two-dimensional t- J model, by using the exact diagonalization technique. At high electron density (for example, 12 electrons in a 4×4 unit cell), S( Q,ω) shows pronounced peak at low energy of order J and is consistent with 2 k f low energy excitations, whereas N( Q,ω) consists of a dense and broad continuum, which is absent from the one-dimensional system. The statistics of elementary charge excitations is also discussed.

Quantum vortices near the superconductor-insulator transition in Josephson junction arrays

We investigate the properties of vortices in Josephson junction arrays in the regime close to the superconductor-insulator transition. We derive general expressions for the vortex mass and the vortex-spinwave coupling in terms of the charge-charge correlation function, which we evaluate in a self consistent harmonic approximation, as well as by means of Monte Carlo simulations. Our main conclusions are that close to the transition to the insulating phase the vortex mass vanishes and the threshold velocity above which vortices couple to spinwaves diverges. Thus, in the quantum regime close to the phase transition there is a velocity window in which vortices may move ballistically without damping, this in contrast to the flux flow behaviour in classical arrays.

Finite-size studies of the neutral-ionic transition in organic mixed-stack compounds.

We have studied the neutral-to-ionic transition in organic charge-transfer compounds in finite-size stacks. To describe these systems we use a model that includes (i) infinite intramolecular Coulomb repulsion, (ii) hybridization between nearest-neighbor molecules (t), and (iii) nearest-neighbor electron-hole attraction (G). Through a recently developed modified Lanczos method we obtain exact numerical results for the following physical quantities: (i) ground-state energy, (ii) occupation of acceptor molecules, (iii) a gap between the ground and first excited state, (iv) a gap between the ground and first triplet excited state, (v) charge-charge and spin-spin correlation functions, and (vi) neutral-ionic parameter phase diagram. The neutral-ionic phase transition is continuous for small G/t and abruptly discontinuous for large G/t, the crossover occurring around G/t\ensuremath{\sim}2. We also study the stability of both phases against dimerization and find that within the model the ionic phase is always unstable against this distortion, while the stability of the neutral phase depends on the value of the rigidity of the stack. We offer a strong-coupling argument that explains this result.

On the a.c. dielectric properties of granular superconductors and the fluctuationally induced reentrant behaviour

The analysis of the temperature and frequency-dependent response function of a granular superconductor is pursued both for the case of a neutral ground state (NGS) and a charge ordered ground state (OGS). In the NGS a fluctuation dominated region is found, showing similar features to the charge-charge correlation function. The obtained analytical expressions for Q(ω) clearly show that the location of the resonances is different in both situations and no-reentrant behaviour is detectable in the charge-correlated ground state.

On the dielectric susceptibility of classical Coulomb systems. II

This paper deals with the shape dependence of the dielectric susceptibility (equivalently defined, in a canonical ensemble, by the mean square fluctuation of the electric polarization or by the second moment of the charge-charge correlation function) of classical Coulomb systems. The concept of partial second moment is introduced with the aim of analyzing the contributions to the total susceptibility of pairs of particles of increasing separation. For a diskshaped one-component plasma with coupling parameter γ=2 it is shown, numerically and algebraically for small and large systems, that (1) the correlation function of two particles close to the edge of the disk decays as the inverse of the square of their distance, and (2) the susceptibility is made up of a bulk contribution, which saturates rapidly toward the Stillinger-Lovett value, and of a surface contribution, which varies on the scale of the disk diameter and is described by a new law called the “arc sine” law. It is also shown that electrostatics and statistical mechanics with shape-dependent thermodynamic limits are consistent for the same model in a strip geometry, whereas the Stillinger-Lovett sum rule is verified for a boundary-free geometry such as the surface of a sphere. Some results of extensive computer simulations of one- and two-component plasmas in circular and elliptic geometries are shown. Anisotropy effects on the susceptibilities are clearly demonstrated and the “arc sine” law for a circular plasma is well confirmed.

Short-range order and phase diagram of a three-dimensional granular superconductor.

The phase diagram of a three-dimensional granular superconductor is explored by calculation of the charge-charge correlation function in the Oguchi approximation. A charge-fluctuation--dominated regime is found, not previously accounted for into the literature. The relevance of phase and/or charge fluctuations is discussed.

Dipole and current fluctuations in the quantum one-component plasma at equilibrium

By an analysis of the current and dipole mean square fluctuations per unit volume for a quantum mechanical jellium in thermal equilibrium at temperature beta -1, the authors give a new proof of the sum rule integral dx mod x mod 2S(x)=3/4(h(cross) omega p/ pi ) coth( beta h(cross) omega p/2) for the second moment of the charge-charge correlation function S(x), where omega p is the plasma frequency. No use is made of perturbation theories. The proof relies on correlation inequalities and sum rules which are valid in phases of charged systems having good screening properties. Up to second order in Planck's constant, the current-current correlations have a non-integrable spatial decay even when the corresponding classical state shows Debye screening.

Thermodynamic and Structural Properties of Charged-Hard-Sphere Mixtures–Application to the Liquid CsAu Alloy

Theories of the excess energy, the Helmholtz free energy, the entropy and the partial and the total structure factors are described on the basis of the charged-hard-sphere model in the mean spherical approximation. In connection wth the charge ordering the important role of the excess entropy is emphasised in addition to that of the charge-charge correlation function. The theories are applied to the liquid CsAu alloy. It is pointed out that the detailed studies of the partial structure factors and the entropy of mixing give the important information on the degree of the charge ordering in the system.

Critical Behaviour of Monatomic and Symmetric Charged Liquids in Approximate Theories of Structure

Abstract A k space analysis of the hypernetted chain (HNC) theory of a monatomic liquid is presented for d dimensions. Assuming the existence of a critical point, the total correlation function is shown to have long-range behaviour proportional to r −2d/3 for short-range interactions. The case of a symmetric charged liquid is then considered in HNC theory and in another approximate treatment of higher-order correlation functions. The number-number structure factor as k → 0 can diverge in both approximate theories whereas the charge-charge structure factor exhibits Debye–Hückel behaviour. The critical ratio (pV/RT)nc Tc is reduced from the superposition approximation value of 1/2 in the monatomic fluid, while in the charged fluid the ‘correction’ to 1/2 involves both number-number and charge-charge correlation functions.

Classical Coulomb systems near a plane wall. II

The equilibrium structure of classical Coulomb systems bounded by a plane hard wall is studied near that wall. A general sum rule is derived for the asymptotic form of the charge-charge correlation function along the wall. The exact results which can be obtained for the two-dimensional one-component plasma provide a test for this new sum rule, as well as for other already known sum rules or their generalizations.

Localised description of valence fluctuations

The authors set up a model for an intermediate valence equivalent to the 'atomic' limit of the Anderson Hamiltonian. Detailed analysis of this model shows that most of the essential characteristics of valence fluctuators are already present in the crudely simplified Hamiltonian. The spin-spin for the 4f charge-charge correlation functions are studied and it is shown that it is possible to define a spin fluctuation frequency omega sf and a charge fluctuation frequency omega cf. omega sf and omega cf differ considerably for some values of the parameters of the model. The magnetic susceptibility and the specific heat are calculated as functions of temperature and it is shown how the results simulate the behaviour found in valence fluctuators.

Phase transitions in the Hubbard Hamiltonian

The authors study phase transitions in the isotropic non-degenerate Hubbard Hamiltonian with renormalization group techniques using the epsilon =4-d expansion to first order in epsilon . The functional obtained from the Hubbard Hamiltonian displays full rotational symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences for the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalisation of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed.

Электронные эффекты в динамической структуре жидких металлов

The partial dynamical structure factors of a pure liquid metal are derived from the two-component theory developed in an earlier paper by March and Tosi. In particular, and in contrast to the usual procedure which assumes the hydrodynamic form for the ion-ion dynamical structureSii(q, ω) to be the same as for a classical one-component liquid, in the present theory the contribution to the sound-wave attenuation from single-particle excitations in the conduction electron system is derived explicitly. It is suggested that this is closely related to the anomalous scaling with isotopic mass of the atomic transport coefficients in liquid lithium. The relation to neutron elastic scattering is also established, and some measurements on liquid gallium can be interpreted in a qualitative manner. By studying the charge-charge correlation function for the two-component liquid metal, a theory of electrical resistivity is afforded, which is shown to reduce to Baym’s treatment of the scattering of electrons by the density fluctuations in the limit of weak electron-ion interaction. The relation between the high-frequency conductivity, obtained for arbitrary strength of the electron-ion interaction and the classical Drude-Zener theory is pointed out, and the sum rules for conductivity are seen to be related to those forSii(q, ω) in the limitq→0. A brief discussion of the thermodynamics of the two-component system is included, and related to results for weak electron-ion coupling.