Slave-boson Method Research Articles

Fano effect and competition between Kondo and antiferromagnetic correlations in doublequantum dots

The influence of the Fano effect and the Kondo and antiferromagnetic (AF) correlations on thetransport properties through a double quantum dot (DQD) structure is investigated by thefinite-U slave-boson mean field method. In the singly-occupied regime, with weakAF correlation, the Fano–Kondo effect greatly reduces the conductanceG no matter whether the transmissivity through the direct channel is high or low, whereas thestrong parity splitting leads to the blockade of the channel through the DQDs. At theparticle–hole symmetric point, when the Kondo and AF correlations are comparable witheach other, their competition results in a resonant conductance peak, which is accompaniedwith a transmission zero due to the Fano effect. This peak-zero structure is a counterpart ofthe characteristic asymmetric line shape and governs the variational trend ofG with the energy levels on dots. The qualitative relations between the positions of thosepeaks and zeros with the transmissivity through the direct channel are obtained via afitting method.

Slave-boson approach to the infinite-UAnderson-Holstein impurity model

The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility is renormalized. From the renormalized charge susceptibility the Kondo temperature is found to increase by the electron-phonon interaction. It turns out that the bosonic 1/N Gaussian fluctuations play a very crucial role, in particular, for the phonon propagator.

Heavy-fermion superconductivity: AnX-boson treatment

We use the X-boson method to study the heavy-fermion superconductivity phase, employing an extension of the periodic Anderson model in the $U=\ensuremath{\infty}$ limit with a nearest-neighbor attractive interaction between the localized f electrons. We show that higher values of the hybridization parameter imply lower values associated with the maximum of the superconducting critical temperature ${T}_{c},$ indicating that the real charge transfer between bands tends to destabilize the Cooper pairing. Moreover, we show that the superconductivity is constrained to the vicinity of a range of densities where the f-band density of states at the Fermi level ${\ensuremath{\rho}}_{f}(\ensuremath{\mu})$ has sufficiently high values, and it was found both for configurations where the system presents intermediate-valence and heavy-fermion behaviors, as experimentally observed. Finally, as the total occupation is raised and for large hybridization parameter V there is an insulator-superconductor transition, which is related to the existence of a hybridization gap that cannot be accessed by the slave-boson method, because when the chemical potential lies in or above the gap the system suffers the second-order phase transition characteristic of that method.

Superconductor–Insulator Transition in thed–pModel

We investigate a transition between the superconducting phase and the Mott insulator phase in the d – p model by using the slave-boson method and the 1/ N -expansion theory, where the pairing interaction is given by the superexchange interaction J s . We show that the competition between the pairing interaction and the Fermi energy induces the transition at finite doping rate.

X-boson cumulant approach to the periodic Anderson model

The Periodic Anderson Model (PAM) can be studied in the infinite U limit by employing the Hubbard X operators to project out the unwanted states. We have already studied this problem employing the cumulant expansion with the hybridization as perturbation, but the probability conservation of the local states (completeness) is not usually satisfied when partial expansions like the Chain Approximation (CHA) are employed. Here we treat the problem by a technique inspired in the mean field approximation of Coleman's slave-bosons method, and we obtain a description that avoids the unwanted phase transition that appears in the mean-field slave-boson method both when the chemical potential is greater than the localized level Ef at low temperatures (T) and for all parameters at intermediate T.

Thermodynamic potential of the periodic Anderson model with the X-boson method: chain approximation

The Periodic Anderson Model (PAM) in the $U\to\infty$ limit has been studied in a previous work employing the cumulant expansion with the hybridization as perturbation (M. S. Figueira, M. E. Foglio and G. G. Martinez, Phys. Rev. B \textbf{50}, 17933 (1994)). When the total number of electrons $N_{t}$ is calculated as a function of the chemical potential $\mu$ in the ``Chain Approximation'' (CHA), there are three values of the chemical potential $\mu$ for each $N_{t}$ in a small interval of $N_{t}$ at low $T$ (M. S Figueira, M. E Foglio, Physica A 208 (1994)). We have recently introduced the ``X-boson'' method, inspired in the slave boson technique of Coleman, that solves the problem of non conservation of probability (completeness) in the CHA as well as removing the spurious phase transitions that appear with the slave boson method in the mean field approximation. In the present paper we show that the X-boson method solves also the problem of the multiple roots of $N_{t}(\mu)$ that appear in the CHA.

Multichannel Electronic Transport Through a Kondo Dot

Electronic transport through the quantum dot with two energy levels is studied by means of the non-equilibrium Green functions and the slave boson method. Special attention is focused on an interplay between quantum inference of traveling waves and electronic correlations. It is shown that if impurity states are far below the Fermi level the transport is through the highest state only. Interference processes become relevant when the levels are shifted towards the mixed valence regime.

Static overscreening and nonlinear response in the Hubbard model

We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down close to the Mott transition. Away from half filling RPA is much less reliable: Already for very small values of the Hubbard interaction U, the linear response becomes much more efficient than RPA, eventually leading to overscreening already beyond quite moderate values of U. To understand this behavior we give a simple argument, which implies that the response to an external perturbation at large U should actually be strongly non-linear. This prediction is confirmed by the results of exact diagonalization.

X-slave boson approach to the periodic Anderson model

The periodic anderson model (PAM) in the limit U=∞, can be studied by employing the Hubbard X operators to project out the unwanted states. In a previous work, we have studied the cumulant expansion of this Hamiltonian employing the hybridization as a perturbation, but probability conservation of the local states (completeness) is not usually satisfied when partial expansions like the “chain approximation (CHA)” are employed. To consider this problem, we use a technique similar to the one employed by Coleman to treat the same problem with slave-bosons in the mean-field approximation. Assuming a particular renormalization for hybridization, we obtain a description that avoids an unwanted phase transition that appears in the mean-field slave-boson method at intermediate temperatures.

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.

Superconductivity in the Hubbard model with pair hopping

The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e. the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1 and d=$\infty$, by means of the (broken symmetry) Hartree-Fock approximations and, for d=$\infty$, by the slave-boson mean-field method. For d=1, at half-filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0 and q=Q ($\eta$-pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings is shrank with increasing lattice dimensionality d and for d=$\infty$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in the both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.

Mean-field magnetic phase diagram of the periodic Anderson model with the Kondo-compensated phases

We have determined the ground-state phase diagram for the periodic Anderson model, which comprises both metallic and insulating collinear magnetic phases with compensated magnetic moments. The compensation is due to both the almost-localized character of f moments and by an equally important Kondo-type polarization of the conduction electrons; it is effective only close to half filling. In such a situation an antiferromagnetic state with very heavy electrons is formed. Thus we introduce a true Kondo-lattice state in a self-consistent manner. The approach is based on the slave-boson method in the saddle-point approximation, in which a strong nonlinear molecular field appears in a natural way. In the polarized state the effective masses are spin dependent. At half filling the antiferromagnetic Kondo insulator evolves with increasing hybridization into a paramagnetic Kondo insulator. We also predict the existence of a weakly ferromagnetic state (with an extremely small net moment) that can be obtained from the antiferromagnetic heavy-fermion state by applying e.g., pressure.

Gutzwiller and slave-boson methods for intersite Coulomb interactions

We investigate the application of the slave-boson method to the treatment of finite intersite interactions. In the saddle-point approximation of the formalism the results obtained with an extended Gutzwiller-type local ansatz are recovered. We discuss the application of the method to a spinless fermion model with nearest-neighbor and long-range Coulomb interactions, respectively.

Slave-Boson Functional-Integral Approach to the Hubbard Model with Orbital Degeneracy

A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy $D$. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate ($D = 2$) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.

Superconductivity in Hubbard Model with Correlated Hopping

Using the slave-boson method in its spinand charge-rotational invariant representation we determine stability of the superconducting state in the Hubbard model with correlated hopping. In general the term with correlated hopping violates electron—hole symmetry, however, in the special case when the correlated hopping integral X is equal to the uncorrelated hopping integral t the electron—hole symmetry remains. We investigate this case and show that correlations induced by onsite Coulomb interactions U yield to the normal state with exactly single occupied sites (corresponding to |U = oo)). The phase diagram of the superconducting state is determined for the different electron concentration n. At the half-filled band (n = 1) a direct transition from the Mott insulator to the superconducting state occurs.

Superconducting properties of the attractive Hubbard model: A slave-boson study.

The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.

Aspects of the normal-state phase of copper oxide planes in high-Tc superconductors.

We examine various aspects of the normal-state phase of Cu${\mathrm{O}}_{2}$ planes in the high-${T}_{c}$ superconductors. In particular, within the context of the three band Hubbard model, we study as a function of doping the competition between a charge density wave phase induced by oxygen breathing modes, antiferromagnetic order, and paramagnetism. To account for the strong electronic interactions, we use the finite $U$ slave boson method of Kotliar and Ruckenstein.

Density of States of Strongly Correlated Electrons in DCNQI-Cu Salts

By making use of the periodic Anderson model with both the electron-phonon interaction and the transverse hopping, we examine the density of states at zero temperature for strongly correlated d electrons in DCNQI-Cu salt which undergoes a metal-insulator transition followed by three-fold periodicity of both a lattice distortion and a local spin. A slave-boson method is applied to the model expressed in terms of a hole picture in order to treat the local constraint strictly. There are both the coherent (band) component and the incoherent (localized) component in the metallic state. In the insulating state, all the electrons at the site with the local spin are incoherent and a small amount of both components remains at other sites.

Electronic States in Strongly Correlated Organic Conductor DCNQI-Cu

Abstract The periodic Anderson model with both the electron-phonon interaction and the interchain hopping has been examined in terms of the slave-boson method to understand the metal-insulator transition in DCNQI(dicyanoquinonediimine)-Cu salts. Strongly correlated states are studied by calculating the phase diagram and the density of states consisting of the incoherent (localized) component and the coherent (band) component.

Electron-phonon induced superconductivity in correlated systems

The issue of electron—phonon induced superconductivity in strongly correlated systems has been discussed. To treat correlation and strong coupling effects we use slave boson method in theU=∞ limit and Eliashberg type of theory. Short range Coulomb interactions severally modify Eliashberg equations making possibles, p andd—wave symmetry of the order parameter. At hole dopings δ≤0.3 andd—wave component of the coupling constant is the largest one.