Anderson localization from the replica formalism

We study Anderson localization in quasi-one-dimensional disordered wires within the framework of the replica sigma model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons, and Zirnbauer, we compute the exact density of transmission matrix eigenvalues of superconducting wires (of symmetry class CI.) For the unitary class of metallic systems (class A) we are able to obtain the density function, save for its large transmission tail.     

Exact solution of a modified periodic Anderson model in one dimension

A periodic Anderson model for electron correlation in a localized-electron band mixed with a conduction band is exactly solved in one dimension, by a Bethe Ansatz, in a modified version with interaction only between right- or left-going wavenumbers. The singlet-ground-state energy for the symmetric model is obtained for the half-filled case N/N_a=2.     

Ground states of a modified symmetric Anderson lattice in one dimension

Based on a previous exact solution of a one-dimensional symmetric Anderson lattice the energy distributions of pseudo-densities of states and the energies of localized and conduction electrons in singlet ground states are calculated. The Kondo-lattice temperature T_KL is obtained as T_KL ≈ (1/2 πUV²)^1/2exp(-/U/2V²) +1/4 πUV².     

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.     

A statistical test of Anderson localization

Numerical demonstrations of localization in random systems are difficult to obtain and interpret because of statistical fluctuations in the electron probability density. This difficulty can be avoided through the use of correlation functions defined in terms of the electron probability density. The fluctuations can then be eliminated by averaging over a large number of Anderson Hamiltonians. The resulting averaged correlation functions clearly show that electrons are exponentially localized. The localization demonstrated here is sufficient to insure a zero dc conductivity in the limit of large systems.     

A self-consistent treatment of Anderson localization

Anderson localization in two-dimensional systems is discussed with the use of Feynman graph method. A self-consistent treatment of diffusion propagator leads to an expression for dynamical conductivity which vanishes at zero frequency while exhibiting well known logarithmic dependence at higher frequency. It is applied to three-dimensional systems, too, and a discussion is given on mobility edge.     

A rigorous block spin approach to massless lattice theories

The renormalization group technique is used to study rigorously the ()⁴ perturbation of the massless lattice field in dimensionsd2. Asymptoticity of the perturbation expansion in powers of is established for the free energy density. This is achieved by using Kadanoff's block spin transformation successively to integrate out high momentum degrees of freedom and by applying ideas previously used by Gallavotti and Balaban in the context of the ultraviolet problems. The method works for arbitrary semibounded polynomials in and .Supported in part by the National Science Foundation under Grant No. PHY 79-16812On leave from Department of Mathematical Methods of Physics, University, PL-00-682 Warsaw, Poland     

A rigorous energy density functional approach

A rigorous approach for constructing of energy density functionals is developed using the local-scale point transformation method. The exact kinetic energy density τ[ρ] contains two terms: the original Weizsäcker term τ_w[ρ] and a Thomas-Fermi-like term τ_w[ρ]. An energy density functionalE[ρ] is built up within a Slater determinant approximation using the most general Skyrme-type forces. It is demonstrated that all Hartree-Fock nuclear ground state results are reproduced quite accurately and consequentlyE[ρ] includes the shell effects accounted mostly by the particular form of τ[ρ]. The approach presented is compared with both Extended Thomas-Fermi and Expectation Value methods. Further possible applications are briefly considered.     

A rigorous approach to Debye screening in dilute classical coulomb systems

The existence and exponential clustering of correlation functions for a dilute classical coulomb system are proven using methods from constructive quantum field theory, the sine gordon transformation and the Glimm, Jaffe, Spencer expansion about mean field theory. This is a vindication of a belief, of long standing amongst physicists, known as Debye screening. This states that, because of special properties of the coulomb potential, the configurations of significant probability are those in which the long range parts ofr ^–1 are mostly cancelled, leaving an effective exponentially decaying potential acting between charge clouds.Supported by N.S.F. Grant PHY 76-17191     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.