Spectral Properties and New Interpolating Solution of Anderson Model

Abstract

A new approach to many-body quasiparticle dynamics of the Anderson impurity model at flnite temperatures is proposed in the framework of the equation-of-motion method. We flnd a new exact identity, which relates the one-particle and many-particle Green functions. Using this identity, it is shown that a new interpolating approximation for the one-particle Green function can be constructed. The approximation which simultaneously reproduces tle weak-coupling limit and the strong coupling limit can be formulated self-consistently. This approach offers a new method for a systematic construction of the approximate interpolating dynamical solutions of strongly correlated electron models.PACS numbers: 67.40. Db, 71.28.+d, 75.20.Hr The problem of an adequate description of strongly correlated electron systems has been studied intensively for the last decade, especially in the context of heavy fermions and high-Τ superconductivity [1]. Theoretical description of strongly correlated electron systems involves simplifled model Hamiltonian. These includes as workable patterns single-impurity Anderson model (SIAM) and Hubbard model. Recently, a lot of effort has been made to gain a better insight into the dynamical properties of the Anderson/Hubbard model [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], especially in the context of many impurities case (e.g. [6]). This field is quite important for description of magnetic properties of anomalous rare-earth compounds [8]. The problem of an adequate and consistent description of dynamics of single-impurity and twoimpurity Anderson models (SIAM and TIAM) and other models of correlated 1attice electrons has not been fully analytically solved yet. The present paper is primarily devoted to the analysis of the relevant many-body dynamical solution of the SIAM and its correct functional structure. We wish to determine which solution actually arises from both the self-consistent many-body approach and intrinsic nature of the model itself. The Hamiltonian of SIAM has the standard form. We will consider single-particle GF of localized electrons. To improve (355) '

Electronic Dynamics of the Anderson Model. The Many-Body Approach

“…In this context it is of interest to consider an interpolating and improved interpolating approximations which were proposed in the papers. 6,7,8,9,10,11,12 We will show that a self-consistent approximation for the SIAM can be formulated which reproduces all relevant exactly solvable limits and interpolates between the strong-and weak-coupling limit. In connection with the dynamical properties the one-particle Green function is the basic quantity to be calculated.…”

“…In this review we discuss the many-body quasiparticle dynamics of the Anderson impurity model 1,2 and its generalizations 3 in the framework of the equation-of-motion method 4,5,6,7,8,9,10,11,12 at finite temperatures. The studies of strongly correlated electrons in solids and their quasiparticle dynamics are intensively explored subjects in solid state physics.…”

“…Hence, it is desirable to have a consistent and closed analytic representation for the one-particle Green function of SIAM. The papers 6,7,8,9,10,11,12 clearly show the importance of the calculation of the Green function and spectral densities for SIAM and the many-impurity Anderson model in a self-consistent way. In this terse overview the problem of consistent analytic description of the many-body dynamics of SIAM is analyzed in the framework of the equation-of-motion approach for double-time thermodynamic Green functions.…”

Quantum Protectorate and Microscopic Models of Magnetism

“…The Hubbard model [12] is in a certain sense an intermediate model (the narrow-band model) and takes into account the specific features of transition metals and their compounds by assuming that the d electrons form a band, but are subject to a strong Coulomb repulsion at one lattice site. The Hubbard Hamiltonian is of the form [26], [27]…”

“…where N is the number of lattice sites. This conceptually simple model is mathematically very complicated [26], [27]. The Pauli exclusion principle which does not allow two electrons of common spin to be at the same site, plays a crucial role.…”