The Barnes slave boson approach to the $U=\infty$ single impurity Anderson model extended by a non-local Coulomb interaction is revisited. We demonstrate first that the radial gauge representation facilitates the treatment of such a non-local interaction by performing the \emph{exact} evaluation of the path integrals representing the partition function, the impurity hole density and the impurity hole density autocorrelation function for a two-site cluster. The free energy is also obtained on the same footing. Next, the exact results are compared to their approximations at saddle-point level, and it is shown that the saddle point evaluation recovers the exact answer in the limit of strong non-local Coulomb interaction, while the agreement between both schemes remains satisfactory in a large parameter range.
We show that a generic single-orbital Anderson impurity model, lacking for instance any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridisation is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetisation of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value $R_\text{W}=2$ in the Kondo r…
We find the dynamical exponent $z = 3$ antiferromagnetic (AF) quantum critical point (QCP) in the heavy fermion quantum transition beyond the standard framework of the Hertz-Moriya-Millis theory with $z = 2$. Based on the U(1) slave-fermion representation of the Anderson lattice model, we show the continuous transition from an antiferromagnetic metal to a heavy fermion Fermi liquid, where the heavy fermion phase consists of two fluids, differentiated from the slave-boson theory. Thermodynamics and transport of the $z = 3$ AF QCP are shown to be consistent with the well known non-Fermi liquid p…
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…
The thermodynamic and transport properties of intermetallic compounds with Ce, Eu, and Yb ions are discussed using the periodic Anderson model with an infinite correlation between $f$ electrons. The slave boson solution of the periodic model shows that the Fermi liquid scale T$_0$ and the Kondo scale T$_K$ depend on the shape of the conduction electrons density of states ($c$ DOS) in the vicinity of the chemical potential, that the details of the band structure determine the ratio T$_0$/T$_K$, and that the crossover between the high- and low-temperature regimes in ordered compounds is system-d…
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 tra…
Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The expectation values of the radial (real) fields are in fact to be interpreted as the density of empty or singly occupied sites. Whereas the radial representation of the Barnes slave bosons has been investigated before, a setup for the functional integral of radial bosonic fields in the more physical Kotliar-Ruckenstein representation has not been accomplished to dat…
We use two different methods, the Hirsch-Fye quantum Monte Carlo simulation and the slave-boson mean field analysis to estimate the effect of spin-orbit coupling on the Kondo temperature in a quantum wire. In quantum Monte Carlo simulation, we calculate the product of spin susceptibility and temperature for different spin-orbit couplings and impurity energies. The variation of the Kondo temperature is estimated via the low temperature universal curves. In the mean field analysis, the Kondo temperature is estimated as the condensation temperature of slave-boson. Both the two methods demonstrate…
The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N)xSU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Taking the Anderson model as an example, these lectures first give an introduction to the auxiliary boson method to describe correlated systems governed by a strong, short-range electronic repulsion. It is then shown how to include the relevant low-lying excitations (coherent sp…
In this paper, we develop a new type of slave particle method which is similar to the slave rotor model except that the quantum rotor is substituted by a spin one slave particle. The spin-one slave particle itself can be represented in terms of Schwinger bosons/fermions. This approach is more conveniently applicable to the strongly correlated Hamiltonians with on-site Hubbard interaction and resolves the limitations of using the slave rotor model as well as the Anderson-Zou slave particle technique. For instance, the mean-field parameters of the slave spin method do not vanish above the Mott t…
In this Letter we study the periodic Anderson model, employing both the slave-boson and the X-boson approaches in the mean field approximation. We investigate the breakdown of the slave-boson at intermediate temperatures when the total occupation number of particles Nt = Nf + Nc is keep constant, where Nf and Nc are respectively the occupation numbers of the localized and conduction electrons, and we show that the high-temperature limit of the slave-boson is Nf = Nc = Nt /2. We also compare the results of the two approaches in the Kondo limit and we show that at low-temperatures the X-boson ex…
It has been recently shown by Nakatsuji, Pines, and Fisk [S. Nakatsuji, D. Pines, and Z. Fisk, Phys. Rev. Lett. 92, 016401 (2004)] from the phenomenological analysis of experiments in Ce1-xLaxCoIn5 and CeIrIn5 that thermodynamic and transport properties of Kondo lattices below coherence temperature can be very successfully described in terms of a two-fluid model, with Kondo impurity and heavy electron Fermi liquid contributions. We analyze thermodynamic properties of Kondo lattices using 1/N slave boson treatment of the periodic Anderson model and show that these two contributions indeed arise…
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 $μ$ in the ``Chain Approximation'' (CHA), there are three values of the chemical potential $μ$ 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-bo…
We revisit the Kotliar-Ruckenstein (KR) slave boson saddle point evaluation for a two-site correlated electron model. As the model can be solved analytically, it is possible to compare the KR saddle point results to the exact many particle levels. The considered two site cluster mimics an infinite-$U$ single-impurity Anderson model with a nearest neighbor Coulomb interaction: one site is strongly correlated with an infinite local Coulomb repulsion which hybridizes with the second site, on which the local Coulomb repulsion vanishes. Making use of the flexibility of the representation we introdu…
We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the …
The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N) x SU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Using an auxiliary boson method, we present a generally applicable scheme to select the relevant contributions in the low frequency regime, while preserving the local gauge symmetry of the model. It amounts to a conserving T-matrix approximation (CTMA) including coherent spin …
Recent studies of dynamical screening of the electronic Coulomb interactions in solids have revived interest in lattice models of correlated fermions coupled to bosonic degrees of freedom (Hubbard-Holstein-type models). We propose a dynamical mean-field-based approach to dynamically screened Coulomb interactions. In the effective Anderson-Holstein model, a transformation to slave rotors [S. Florens and A. Georges, Phys. Rev. B 66, 165111 (2002)] is performed to decouple the dynamical part of the interaction. This transformation allows for a systematic derivation and analysis of recently introd…
We investigated electron phases in the $f^2$-configuration system with the $Γ_1$ crystalline-electric-field (CEF) ground state in cubic symmetry. An extended three-orbital periodic Anderson model, which consists of $j=5/2$ states, is evaluated by using the rotationally invariant slave boson formalism. As a result, we found three phases at zero temperature: the $Γ_1$ CEF singlet phase, and two kinds of Fermi liquid (FL). One of the FL arises owing to the presence of the $Γ_5$ CEF state, while the other forms a quasi-degenerated CEF state. All these phases are separated by first-order transition…
We introduce a representation of electron operators as a product of a spin-carry ing fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a new method is proposed for solving multi-orbital Anderson quantum impurity models at finite interaction strength U. It consists in a set of coupled integral equations for the auxiliary field Green's functions, which can be derived from a controlled saddle-point in the limit of a large number of field components. In contrast to some finite-U extensions of the non-crossing approximation, the new method…
We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green's function of the physical electron and the projected Green's function of the pseudofermion coincide. Correlation and Green's functions in the spinful case involve a complex entanglement of the world lines which, however, can be …
We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the…
A rational representation for the self-energy is explored to interpolate the solution of the Anderson impurity model in general orbitally degenerate case. Several constrains such as the Friedel's sum rule, high--frequency moments and the value of quasiparticle residue are used to establish the equations for the coefficients of the interpolation. We test two fast techniques, the slave--boson mean--field and the Hubbard I approximation to determine the coefficients. The obtained self--energies are compared with the results of numerically exact Quantum Monte Carlo method. We find that using the s…
We review a recently developed method, based on a pseudoparticle representation of correlated electrons, to describe both Fermi liquid and non-Fermi liquid behavior in quantum impurity systems. The role of the projection onto the physical Hilbert space and the impossibility of slave boson condensation are discussed. By summing the leading coherent spin and charge fluctuation processes in a fully self-consistent and gauge invariant way one obtains the correct infrared behavior of the pseudoparticles. The temperature dependence of the spin susceptibility for the single channel and two-channel An…
Results are presented for the nonequilibrium infinite-U Anderson model using a large-N approach, where $N$ is the degeneracy of the impurity level, and where nonequilibrium is established by coupling the level to two leads at two different chemical potentials so that there is current flow. A slave-boson representation combined with Keldysh functional integral methods is employed. Expressions for the static spin susceptibility $χ_S$ and the conductance $G$ are presented to ${\cal O}(\frac{1}{N})$ and for an applied voltage difference $V$ less than the Kondo temperature. The correlation function…
It has been recently shown that the particle-hole symmetric Anderson impurity model can be mapped onto a $Z_2$ slave-spin theory without any need of additional constraints. Here we prove by means of Numerical Renormalization Group that the slave-spin behaves in this model like a two-level system coupled to a sub-ohmic dissipative environment. It follows that the $Z_2$ symmetry gets spontaneously broken at zero temperature, which we find can be identified with the on-set of Kondo coherence, being the Kondo temperature proportional to the square of the order parameter. Since the model is numeric…
A rational representation for the self--energy is explored to interpolate the solution of the Anderson impurity model in general orbitally degenerate case. Several constrains such as the Friedel's sum rule, positions of the Hubbard bands as well as the value of quasiparticle residue are used to establish the equations for the coefficients of the interpolation. We employ two fast techniques, the slave--boson mean--field and the Hubbard I approximations to determine the functional dependence of the coefficients on doping, degeneracy and the strength of the interaction. The obtained spectral func…
Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the $\mathbb{Z}_2$ slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resultin…
Using the constrained-path Monte Carlo method, we studied the magnetic properties of the two-dimensional periodic Anderson model for electron fillings between 1/4 and 1/2. We also derived two effective low energy theories to assist in interpreting the numerical results. For 1/4 filling we found that the system can be a Mott or a charge transfer insulator, depending on the relative values of the Coulomb interaction and the charge transfer gap between the two non-interacting bands. The insulator may be a paramagnet or antiferromagnet. We concentrated on the effect of electron doping on these ins…
We propose a new method of solving a class of mean-field (MF) models, which is based on the Maximum Entropy (MaxEnt) principle with additional constraints included. Next, we show equivalence of our method when applied to the Gutzwiller approximation (GA), with the mean-field slave-boson (SB) formalism (on the example of the single-band Hubbard model). This equivalence provides thus an alternative justification of the results obtained within the SB approach which, however, contains ad hoc assumptions to position it in agreement with GA. Our approach implies that all predictions of the MF SB met…
We introduce a strongly correlated mean-field theory of the ionic Hubbard model on the triangular lattice with alternating stripes of site energy using Barnes-Coleman slave bosons. We study the paramagnetic phases of this theory at three quarters filling, where it is a model of Na_0.5CoO_2, Rb_0.5CoO_2, and K_0.5CoO_2. This theory has two bands of fermionic quasi-particles: one of which is filled or nearly filled and hence weakly correlated; the other is half-filled or nearly half-filled and hence strongly correlated. Further results depend strongly on the sign of the hopping integral, t. The …
Properties of an extended periodic Anderson model with the f-c Coulomb interaction $\Ufc$ is studied as a model for \Ge and related compounds which is cosidered to exhibit a sharp valence change under pressure. The problem is treated by extending the {\it slave-boson} and large-N expansion method to treat the present system. It is shown that, as the f-level $ε_{\rm f}$ is increased relative to the Fermi level, the sharp valence change is caused by the effect of $\Ufc$ with moderate strength of the order of the bandwith of conduction electrons. The superconducting transition temperature $T_\rc$…
Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce "symplectic Hubbard operators": an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-cohere…
Both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. In an Anderson box, mesoscopic fluctuations of the effective single particle properties will be large. We study how the statistical fluctuations at low temperature in these two problems are connected, using random matrix theory and the slave boson mean field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Secon…
An SU(2) slave boson formulation of bond-type spin nematic orders is developed in frustrated ferromagnets, where the spin nematic states are described as the resonating spin-triplet valence bond (RVB) states. The d-vectors of spin-triplet pairing ansatzes play the role of the directors in the bond-type spin quadrupolar states. The low-energy excitations around such spin-triplet RVB ansatzes generally comprise the (potentially massless) gauge bosons, massless Goldstone bosons, and spinon individual excitations. Extending the projective symmetry group argument to the spin-triplet ansatzes, we sh…
The infinite-$U$ Anderson model coupled to a Jahn-Teller phonon is studied using the slave boson method on the basis of the large degeneracy expansion (1/N) scheme. The model Hamiltonian acts on the orbital degrees of freedom. The main focus is on the interplay between strong local electron correlation and weak Jahn-Teller electron-phonon interaction. The Kondo temperature is found to decrease by Jahn-Teller interaction. The influence of the Jahn-Teller interaction on dynamical correlation functions is very significant in sharp contrast with the case of the Holstein-type phonon which couples t…
We introduce Gutzwiller-correlated wave functions for the variational investigation of general multi-band Hubbard models. We set up a diagrammatic formalism which allows us to evaluate analytically ground-state properties in the limit of infinite spatial dimensions. In this limit recent results obtained within the Gutzwiller approximation are seen to become exact for these wave functions. We further show that the Slave Boson mean-field theory for degenerate bands becomes variationally controlled at zero temperature in infinite dimensions. Lastly, we briefly comment on the variational approach …
The non-interacting and non-Hermitian, parity-time ($\mathcal{PT}$)-symmetric Anderson model exhibits an exceptional point (EP) at a non-Hermitian coupling $g=1$, which remains unrenormalized in the presence of interactions (Lourenco et al, arXiv:1806.03116), where the EP was shown to coincide with the quantum critical point (QCP) for Kondo destruction. In this work, we consider a quantum dot hybridizing with metallic leads having Rashba spin-orbit coupling ($λ$). We show that for a non-Hermitian hybridization, $λ$ can renormalize the exceptional point even in the non-interacting case, stabili…
Electron transport between two superconductors through an Anderson impurity in the Kondo regime is investigated within the slave boson mean field approximation. The current, shot noise power and Fano factor are displayed versus the applied bias voltage in the subgap region and found to be strongly dependent on the ratio between the Kondo temperature $T_{K}$ and the superconducting gap $Δ$. In particular, the $I-V$ curve exposes an excess current in the limit $T_{K}/Δ\gg 1$.
Kondo breakdown induced by non-Hermitian complex hybridization
Research Institute for Innovation and Co-Creation, Osaka Metropolitan University（大阪公立大学创新与共创研究所）；Department of Physics, Osaka Metropolitan University（大阪公立大学物理系）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学南部阳一郎理论实验物理研究所）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Department of Physics, University of Tokyo（东京大学物理系）；Fundamental Quantum Science Program, TRIP Headquarters, RIKEN（理化学研究所TRIP总部基础量子科学项目）；Department of Physics, Ritsumeikan University（立命馆大学物理系）；Department of Materials Engineering Science, University of Osaka（大阪大学材料工程科学系）
We study an impurity Anderson model to describe an iron phthalocyanine (FePc) molecule on Au(111), motivated by previous results of scanning tunneling spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet consisting in one hole at the $3d_{z^2}$ orbital of iron and two degenerate doublets corresponding to one hole either in the $3d_{xz}$ or in the $3d_{yz}$ orbital (called $π$ orbitals) with two degenerate Hund-rule triplets with one hole in the $3d_{z}$ orbital and another one in a $π$ orbital. We solve the model using a slave-boson mean-field approximation (SBMFA). …
A system of two interacting cobalt atoms, at varying distances, was studied in a recent scanning tunneling microscope experiment by Bork et. al.[Nature Phys. 7, 901 (2011)]. We propose a microscopic model that explains, for all experimentally analyzed interatomic distances, the physics observed in these experiments. Our proposal is based on the two-impurity Anderson model, with the inclusion of a two-path geometry for charge transport. This many-body system is treated in the finite-U slave boson mean-field approximation and the logarithmic-discretization embedded-cluster approximation. We phys…
