Projective quantum monte carlo method for the anderson impurity model and its application to dynamical mean field theory

We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the frustrated one-band Hubbard model, reconfirming the numerical renormalization group results.     

Curie temperature in the Hubbard model with alloy disorder

Magnetic and electric properties of the Hubbard model with binary alloy disorder are studied within the dynamical mean-field theory. A paramagnet-ferromagnet phase transition and a Mott-Hubbard metal-insulator transition are observed upon varying the alloy concentration. A disorder induced enhancement of the Curie temperature is demonstrated and explained by the effects of band splitting and subband filling.     

Effect of particle-hole asymmetry on the Mott-Hubbard metal-insulator transition

The Mott-Hubbard metal-insulator transition is one of the most important problems in correlated-electron systems. In the past decade, much progress has been made in examining a particle-hole symmetric form of the transition in the Hubbard model with dynamical mean field theory, where it was found that the electronic self-energy develops a pole at the transition. We examine the particle-hole asymmetric metal-insulator transition in the Falicov-Kimball model and find that a number of features change when the noninteracting density of states has a finite bandwidth.     

Nature of the Peierls- to Mott-insulator transition in 1D

In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across a narrow intermediate phase with finite spin, charge, and optical excitation gaps. Received 7 July 2002 / Received in final form 21 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: holger.fehske@physik.uni-greifswald.de     

Features of the conductivity and magnetoresistance of doped two-dimensional structures near a metal-insulator transition

Theoretical and experimental studies of the conductivity and magnetoresistance of selectively doped structures of GaAs/AlGaAs quantum well structures near a metal-insulator phase transition have been reviewed. Special attention is focused on the role of the structure of impurity bands, which are narrow in the absence of intentional compensation and, in the case of doping of barriers, include the partially filled upper Hubbard band. It has been shown that the indicated structures exhibit (i) specific mixed conductivity, which can, in particular, include the contribution from delocalized states in the impurity band; (ii) the virtual Anderson transition, which is suppressed with an increase in disorder owing to compensation or with an increase in the concentration of a dopant; (iii) slow relaxations of the hopping magnetoresistance caused by the Coulomb glass effects, including, in particular, the states of the upper Hubbard band; and (iv) the suppression of the negative interference magnetoresistance owing to the spin effects.     

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for L ≤ 14 lattice results in a continuous Mott-Hubbard transition at U_c≈W. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.     

Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.     

Hund’s coupling and the metal-insulator transition in the two-band Hubbard model

The Mott-Hubbard metal-insulator transition is investigated in a two-band Hubbard model within dynamical mean-field theory. To this end, we use a suitable extension of Wilsons numerical renormalization group for the solution of the effective two-band single-impurity Anderson model. This method is non-perturbative and, in particular, allows to take into account the full exchange part of the Hunds rule coupling between the two orbitals. We discuss in detail the influence of the various Coulomb interactions on thermodynamic and dynamic properties, for both the impurity and the lattice model. The exchange part of the Hunds rule coupling turns out to play an important role for the physics of the two-band Hubbard model and for the nature of the Mott-transition.     

Observation of disorder-induced 2D mott-hubbard states of the alkali-earth metal (Mg,Ba)-adsorbed Si(111) surface

We report evidence of a disorder-driven Mott-Hubbard-type localization on the alkali-earth metal (AEM) (Mg,Ba)-adsorbed Si(111)-(7x7) surface. The clean metallic Si(111) surface is found to undergo a two-dimensional (2D) metal-insulator transition as randomly distributed AEM adsorbates cause disorder on the surface. A well-defined electron-energy-loss peak unique to the insulating phase is attributed to an interband excitation between the split Hubbard bands originated from a metallic surface band at Fermi energy. A quantitative analysis of the loss peak reveals that the AEM-induced insulating surfaces are of a Mott-Hubbard type driven essentially by disorder.     

Non-Fermi-liquid behavior in the periodic anderson model

We study the Mott metal-insulator transition in the periodic Anderson model with dynamical mean field theory (DMFT). Near the quantum transition, we find a non-Fermi-liquid metallic state down to a vanishing temperature scale. We identify the origin of the non-Fermi-liquid behavior as being due to magnetic scattering of the doped carriers by the localized moments. The non-Fermi-liquid state can be tuned by either doping or external magnetic field. Our results show that the coupling to spatial magnetic fluctuations (absent in DMFT) is not a prerequisite to realizing a non-Fermi-liquid scenario for heavy fermion systems.     

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition

The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a mean-field approach which is interesting conceptually: Trial self-energies from a two-site single-impurity Anderson model are used to evaluate an exact and general variational principle. While this restriction of the domain of the functional represents a strong approximation, the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the linearized DMFT which has been suggested previously as a handy approach to study the critical regime close to the transition. It turns out that the two-site approximation is able to reproduce the complete (zero and finite-temperature) phase diagram for the Mott transition. For the critical point at T = 0, the entire calculation can be done analytically. This calculation elucidates different general aspects of the self-energy-functional theory. Furthermore, it is shown how to deal with a number of technical difficulties which appear when the self-energy functional is evaluated in practice.Received: 3 November 2003, Published online: 23 December 2003PACS: 71.10.-w Theories and models of many-electron systems - 71.15.-m Methods of electronic structure calculations - 71.30. + h Metal-insulator transitions and other electronic transitions     

Magnetic and dynamic properties of the Hubbard model in infinite dimensions

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular, we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the Néel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon asn<1. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.     

“Linearized” dynamical mean-field theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The “linearized DMFT” yields plausible results for the complete geometry dependence of the critical interaction. Received 6 May 1999 and Received in final form 2 July 1999     

Metal-insulator transition in the Hubbard model with incommensurate magnetic structures

The metal-insulator transition for the square, simple cubic, and body centered cubic lattices has been studied within the Hubbard model at half-filling taking into account nearest- and next-nearest-neighbor electron hopping. Both staggered antiferromagnetic and incommensurate magnetic states (spin-spiral wave) have been considered. The inclusion of the latter states for the three-dimensional lattices does not change the general pattern of the metal-insulator transition, but opens the fundamentally new possibility of the metal-insulator transition of the first order between the magnetically ordered states for the square lattice.     

Effect of conduction-electron interaction in the Falicov-Kimball model

The effect of conduction-electron interaction on the pressure-induced first order metal-insulator transition is investigated within a two-band Hubbard model. Results are presented for two mean-field-type approximations which show a change in the critical pressure and the conduction-electron occupation number at the transition.     

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition. The text was submitted by the authors in English.     

Splitting of the lower subband of Hubbard fermions in the Shubin–Vonsowsky model under the influence of strong intersite correlations

The diagram technique for Hubbard operators is used to investigate the influence of intersite Coulomb interactions on the energy structure and Cooper instability of strongly correlated fermions. Allowance for intersite correlations in doped Mott-Hubbard insulators is shown to lead to a splitting of the lower subband of Hubbard fermions and to the formation of a band of fluctuation states as soon as the intersite interaction energy becomes comparable to or exceeds the mean kinetic energy. The spectral intensity of the splitoff band is proportional to the root-mean-square fluctuation of the occupation numbers and increases with doping level. The predicted effect changes significantly the structure of the density of electronic states. This leads to a renormalization of the pole of the scattering amplitude in the Cooper channel and manifests itself as a nonuniform (in electron concentration) modification of the dependence of the critical superconducting transition temperature.     

Correlations and conductivity of interacting fermions in a disordered chain—a Monte Carlo simulation

The interplay between disorder and interaction in a one dimensional system of fermions is investigated by the use of a Monte Carlo simulation. The model considered (Hubbard Anderson Model) is a combination of the Anderson model, for noninteracting fermions in a random potential, and the extended Hubbard model, for interacting fermions in a periodic potential. To study the physics of this model, a (Quantum) Monte Carlo simulation is performed for a finite chain of 120 sites. The simulation is done for different band fillings, and several values of the interaction parameters and the strength of disorder. The low frequency behaviour of the conductivity is calculated as well as the static correlation functions for the charge density and the spin density. From the results for these quantities the competition between disorder-induced effects (Anderson localization) and interaction-induced effects (Mott transition, long range order) is studied.     

Similarities between the hubbard and periodic anderson models at finite temperatures

The single band Hubbard and the two band periodic Anderson Hamiltonians have traditionally been applied to rather different physical problems-the Mott transition and itinerant magnetism, and Kondo singlet formation and scattering off localized magnetic states, respectively. In this paper, we compare the magnetic and charge correlations, and spectral functions, of the two systems. We show quantitatively that they exhibit remarkably similar behavior, including a nearly identical topology of the finite temperature phase diagrams at half filling. We address potential implications of this for theories of the rare earth "volume collapse" transition.     

From mixed valence to the Kondo lattice regime

Many heavy fermion materials are known to cross over from the Kondo lattice regime to the mixed valence regime or vice versa as a function of pressure or doping. We study this crossover theoretically by employing the periodic Anderson model within the framework of the dynamical mean field theory. Changes occurring in the dynamics and transport across this crossover are highlighted. As the valence is decreased (increased) relative to the Kondo lattice regime, the Kondo resonance broadens significantly, while the lower (upper) Hubbard band moves closer to the Fermi level. The resistivity develops a two peak structure in the mixed valence regime: a low temperature coherence peak and a high temperature 'Hubbard band' peak. These two peaks merge, yielding a broad shallow maximum upon decreasing the valence further. The optical conductivity likewise exhibits an unusual absorption feature (shoulder) in the deep mid-infrared region, which grows in intensity with decreasing valence. The involvement of the Hubbard bands in dc transport and of the effective f-level in the optical conductivity are shown to be responsible for the anomalous transport properties. A two-band hybridization-gap model, which neglects incoherent effects due to many-body scattering, commonly employed to understand the optical response in these materials is shown to be inadequate, especially in the mixed valence regime. Comparison of theory with experiment carried out for (a) dc resistivities of CeRhIn(5), Ce(2)Ni(3)Si(5), CeFeGe(3) and YbIr(2)Si(2), (b) pressure dependent resistivity of YbInAu(2) and CeCu(6), and (c) optical conductivity measurements in YbIr(2)Si(2) yields excellent agreement.