Electron Correlations and Materials Properties, 1999
We study electronic properties of solids with correlated d electrons which could be described by ... more We study electronic properties of solids with correlated d electrons which could be described by a multiband Hubbard Hamiltonian in the weak-interaction case, U/w < 1. The one-electron part of the many-body Hamiltonian is described by a tight-binding LMTO method. The many-body part is treated by non-selfconsistent FLEX-type approximations with adjusted chemical potential not to change the LMTO band filling. The calculated DOS gets narrower but is only little influenced by electron correlations at the Fermi energy. A precursor of a satellite band in the paramagnetic bcc Ni is found at about 6 eV below the Fermi level in agreement with experiment.
We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and ... more We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing "Kondo" scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metalinsulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.
We study the influence of disorder and randomly distributed impurities on the properties of corre... more We study the influence of disorder and randomly distributed impurities on the properties of correlated antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed.
We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of rep... more We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of replica-symmetry breaking below the transition temperature to the glassy phase. We find that the ordered phase is degenerate and solutions with one hierarchy of spin replicas and with the full continuous replica-symmetry breaking coexist for p > p * ≈ 2.82. The latter emerges immediately with the instability of the replica-symmetric one. Apart from these two solutions there exists also a succession of unstable states converging to the solution with the continuous replica-symmetry breaking that is marginally stable and has the highest free energy.
We report a theoretical investigation of the electronic structure of the plutonium-based medium-h... more We report a theoretical investigation of the electronic structure of the plutonium-based medium-high-T c superconductor PuCoGa 5 , on the basis of ab initio local spin-density functional calculations. We furthermore report electronic structure calculations of the related actinide compounds PuRhGa 5 , PuIrGa 5 , UCoGa 5 , NpCoGa 5 , and AmCoGa 5. PuRhGa 5 is a superconductor as well, whereas the other materials do not become superconducting. The equilibrium lattice parameters within the tetragonal HoCoGa 5 crystal structure are well reproduced for UCoGa 5 , NpCoGa 5 , as well as for the three isoelectronic Pu-115 compounds when we assume delocalized 5f states. The possibility of a partial 5f localization occurring for the Pu-115 compounds is discussed. The electronic structures of the three Pu-115 compounds are computed to be rather similar: in each of the Pu-115 materials the density of states at the Fermi energy is dominated by the Pu 5f contribution. Our total-energy calculations predict antiferromagnetic order to be favorable for all three Pu-115 materials, which is, however, observed experimentally for PuIrGa 5 only. Within the Pu-115 series some small changes of the bands near the Fermi energy occur, which could be relevant for the superconductivity. A comparison of the ab initio calculated and the experimental properties clearly supports the picture of delocalized 5f electrons for UCoGa 5. The neptunium-based 115 compound is predicted to order antiferromagnetically, which is supported by experiment. Also, the calculated magnetic moment ͑0.85 B ͒ compares well with the measured moment ͑0.84 B ͒. These findings advocate that the Np 5f's are still to some extent delocalized in NpCoGa 5. In contrast, for the Am-115 analog the Am 5f electrons can be expected to be localized. We furthermore discuss the theoretical Fermi surfaces and present calculated de Haas-van Alphen quantities for a comparison with future experiments. For UCoGa 5 we obtain a semi-quantitative agreement with recently reported de Haas-van Alphen experiments. The possible origins of the superconductivity are discussed. Our investigation particularly reinforces the analogy to the heavy-fermion superconductors CeCoIn 5 and CeIrIn 5 , however, with a stronger coupling strength due to a much stronger 5f hybridization.
We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a s... more We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.
We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite inte... more We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite interval to the X-ray edge problem. Dyson equations for basic Green functions from the X-ray problem are rewritten as convolutive integral equations on a time-interval [0,t] with t→∞. The long-time asymptotics of solutions to these equations is derived with the aid of the Wiener–Hopf method. Although the Wiener–Hopf long-time exponents differ by a factor of two from the solution of Nozières and De Dominicis we demonstrate how the latter and the critical exponents of measurable amplitudes from the X-ray problem can be derived from the former. We explain that the difference in the exponents arises due to different ways of performing the long-time limit in the two solutions. To enable the infinite-time limit in the defining equations a new infinite-time scale τ→∞, interpreted as an effective lifetime of the core-hole, must be introduced. The ratio t/τ decides about the resulting critical expone...
We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model.... more We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.
The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagr... more The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.
arXiv: Disordered Systems and Neural Networks, 2015
We address the problem of vanishing of diffusion in noninteracting disordered electron systems an... more We address the problem of vanishing of diffusion in noninteracting disordered electron systems and its description by means of averaged Green functions. Since vanishing of diffusion, Anderson localization, cannot be identified by means of one-electron quantities, one must appropriately approximate two-particle functions. We show how to construct nontrivial and self-consistent approximations for irreducible vertices and to handle them so that the full dynamical Ward identity and all macroscopic conservation laws are obeyed. We derive an approximation-free low-energy representation of the full two-particle vertex that we use to calculate the critical part of the electron-hole correlation function, the diffusion pole and the dynamical diffusion constant. We thereby pave the way for a systematic and controllable description of vanishing of diffusion in disordered systems.
We present a detailed, quantitative study of the competition between interaction- and disorder-in... more We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the N\'{e}el-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.
The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a clo... more The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the free energy as a functional of order parameters. Then we set stationarity equations for local maxima of the free energy determining the order-parameter function on interval [0,1]. Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.
We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet a... more We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet approach to determine the electron-hole and electron-electron irreducible vertices self-consistently. We demonstrate that when the dominant contributions from the critical region of the singularity driven by multiple electron-hole scatterings are properly taken into account we make the parquet equations soluble and recover the Kondo asymptotics in the symmetric as well as in the asymmetric cases.
The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. ... more The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. In this limit the coupled Bethe-Salpeter equations determining two-particle vertices (parquet equations) reduce to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signaling vanishing of electron diffusion and onset of Anderson localization. There is no bifurcation in d=1,2 where all states are localized. In dimensions d>=3 the mobility edge separating metallic and insulating phase is found for various types of disorder and compared with results of other treatments.
Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singul... more Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singularity due to Mahan [Phys. Rev. 163 (1967) 612] and Nozières and De Dominicis [Phys. Rev. 178 (1969) 1097] are compared. We analyze the conditions under which these methods deliver a unique (exact) solution. Two large (infinite) time scales must be introduced to distinguish the methods, relaxation time T and an effective lifetime of the excited electron hole pair tau. It is shown that the edge behavior depends on the ratio T/tau being zero in the Fredholm and infinity in the Wiener Hopf approach.
Electron Correlations and Materials Properties, 1999
We study electronic properties of solids with correlated d electrons which could be described by ... more We study electronic properties of solids with correlated d electrons which could be described by a multiband Hubbard Hamiltonian in the weak-interaction case, U/w < 1. The one-electron part of the many-body Hamiltonian is described by a tight-binding LMTO method. The many-body part is treated by non-selfconsistent FLEX-type approximations with adjusted chemical potential not to change the LMTO band filling. The calculated DOS gets narrower but is only little influenced by electron correlations at the Fermi energy. A precursor of a satellite band in the paramagnetic bcc Ni is found at about 6 eV below the Fermi level in agreement with experiment.
We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and ... more We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing "Kondo" scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metalinsulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.
We study the influence of disorder and randomly distributed impurities on the properties of corre... more We study the influence of disorder and randomly distributed impurities on the properties of correlated antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed.
We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of rep... more We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of replica-symmetry breaking below the transition temperature to the glassy phase. We find that the ordered phase is degenerate and solutions with one hierarchy of spin replicas and with the full continuous replica-symmetry breaking coexist for p > p * ≈ 2.82. The latter emerges immediately with the instability of the replica-symmetric one. Apart from these two solutions there exists also a succession of unstable states converging to the solution with the continuous replica-symmetry breaking that is marginally stable and has the highest free energy.
We report a theoretical investigation of the electronic structure of the plutonium-based medium-h... more We report a theoretical investigation of the electronic structure of the plutonium-based medium-high-T c superconductor PuCoGa 5 , on the basis of ab initio local spin-density functional calculations. We furthermore report electronic structure calculations of the related actinide compounds PuRhGa 5 , PuIrGa 5 , UCoGa 5 , NpCoGa 5 , and AmCoGa 5. PuRhGa 5 is a superconductor as well, whereas the other materials do not become superconducting. The equilibrium lattice parameters within the tetragonal HoCoGa 5 crystal structure are well reproduced for UCoGa 5 , NpCoGa 5 , as well as for the three isoelectronic Pu-115 compounds when we assume delocalized 5f states. The possibility of a partial 5f localization occurring for the Pu-115 compounds is discussed. The electronic structures of the three Pu-115 compounds are computed to be rather similar: in each of the Pu-115 materials the density of states at the Fermi energy is dominated by the Pu 5f contribution. Our total-energy calculations predict antiferromagnetic order to be favorable for all three Pu-115 materials, which is, however, observed experimentally for PuIrGa 5 only. Within the Pu-115 series some small changes of the bands near the Fermi energy occur, which could be relevant for the superconductivity. A comparison of the ab initio calculated and the experimental properties clearly supports the picture of delocalized 5f electrons for UCoGa 5. The neptunium-based 115 compound is predicted to order antiferromagnetically, which is supported by experiment. Also, the calculated magnetic moment ͑0.85 B ͒ compares well with the measured moment ͑0.84 B ͒. These findings advocate that the Np 5f's are still to some extent delocalized in NpCoGa 5. In contrast, for the Am-115 analog the Am 5f electrons can be expected to be localized. We furthermore discuss the theoretical Fermi surfaces and present calculated de Haas-van Alphen quantities for a comparison with future experiments. For UCoGa 5 we obtain a semi-quantitative agreement with recently reported de Haas-van Alphen experiments. The possible origins of the superconductivity are discussed. Our investigation particularly reinforces the analogy to the heavy-fermion superconductors CeCoIn 5 and CeIrIn 5 , however, with a stronger coupling strength due to a much stronger 5f hybridization.
We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a s... more We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.
We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite inte... more We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite interval to the X-ray edge problem. Dyson equations for basic Green functions from the X-ray problem are rewritten as convolutive integral equations on a time-interval [0,t] with t→∞. The long-time asymptotics of solutions to these equations is derived with the aid of the Wiener–Hopf method. Although the Wiener–Hopf long-time exponents differ by a factor of two from the solution of Nozières and De Dominicis we demonstrate how the latter and the critical exponents of measurable amplitudes from the X-ray problem can be derived from the former. We explain that the difference in the exponents arises due to different ways of performing the long-time limit in the two solutions. To enable the infinite-time limit in the defining equations a new infinite-time scale τ→∞, interpreted as an effective lifetime of the core-hole, must be introduced. The ratio t/τ decides about the resulting critical expone...
We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model.... more We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.
The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagr... more The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.
arXiv: Disordered Systems and Neural Networks, 2015
We address the problem of vanishing of diffusion in noninteracting disordered electron systems an... more We address the problem of vanishing of diffusion in noninteracting disordered electron systems and its description by means of averaged Green functions. Since vanishing of diffusion, Anderson localization, cannot be identified by means of one-electron quantities, one must appropriately approximate two-particle functions. We show how to construct nontrivial and self-consistent approximations for irreducible vertices and to handle them so that the full dynamical Ward identity and all macroscopic conservation laws are obeyed. We derive an approximation-free low-energy representation of the full two-particle vertex that we use to calculate the critical part of the electron-hole correlation function, the diffusion pole and the dynamical diffusion constant. We thereby pave the way for a systematic and controllable description of vanishing of diffusion in disordered systems.
We present a detailed, quantitative study of the competition between interaction- and disorder-in... more We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the N\'{e}el-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.
The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a clo... more The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the free energy as a functional of order parameters. Then we set stationarity equations for local maxima of the free energy determining the order-parameter function on interval [0,1]. Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.
We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet a... more We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet approach to determine the electron-hole and electron-electron irreducible vertices self-consistently. We demonstrate that when the dominant contributions from the critical region of the singularity driven by multiple electron-hole scatterings are properly taken into account we make the parquet equations soluble and recover the Kondo asymptotics in the symmetric as well as in the asymmetric cases.
The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. ... more The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. In this limit the coupled Bethe-Salpeter equations determining two-particle vertices (parquet equations) reduce to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signaling vanishing of electron diffusion and onset of Anderson localization. There is no bifurcation in d=1,2 where all states are localized. In dimensions d>=3 the mobility edge separating metallic and insulating phase is found for various types of disorder and compared with results of other treatments.
Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singul... more Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singularity due to Mahan [Phys. Rev. 163 (1967) 612] and Nozières and De Dominicis [Phys. Rev. 178 (1969) 1097] are compared. We analyze the conditions under which these methods deliver a unique (exact) solution. Two large (infinite) time scales must be introduced to distinguish the methods, relaxation time T and an effective lifetime of the excited electron hole pair tau. It is shown that the edge behavior depends on the ratio T/tau being zero in the Fredholm and infinity in the Wiener Hopf approach.
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Papers by V. Janis