Quasiaverages, symmetry breaking and irreducible Green functions method

Abstract

The development and applications of the method of quasiaverages to quantum statistical physics and to quantum solid state theory and, in particular, to quantum theory of magnetism, were considered. It was shown that the role of symmetry (and the breaking of symmetries) in combination with the degeneracy of the system was reanalyzed and essentially clarified within the framework of the method of quasiaverages. The problem of finding the ferromagnetic, antiferromagnetic and superconducting "symmetry broken" solutions of the correlated lattice fermion models was discussed within the irreducible Green functions method. A unified scheme for the construction of generalized mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the equations of motion and Dyson equation was generalized in order to include the "source fields". This approach complements previous studies of microscopic theory of antiferromagnetism and clarifies the concepts of Neel sublattices for localized and itinerant antiferromagnetism and "spin-aligning fields" of correlated lattice fermions. 05.30.Fk,

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

“…When working with infinite hierarchies of equations for Green functions 4,5 the main problem is finding the methods for their efficient decoupling, with the aim of obtaining a closed system of equations, which determine the Green functions. In the papers 32,78,79,80,81 devoted to studies of lattice systems of interacting fermions it was shown that for a wide range of problems in statistical mechanics 82,83,84,85 and theory of condensed matter one can outline a fairly systematic recipe for constructing approximate solutions in the framework of irreducible Green functions method. Within this approach one can look from a unified point of view at the main problems of fundamental characters arising in the method of two-time temperature Green functions.…”

“…The important point about equations ( 82), (83) is that any approximate solution of SIAM should be consistent with it. Let us remind how to get solution (82). It follows from the system of equations for small-V limit:…”

“…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. 4,5 In addition to the irreducible Green functions (IGF) approach, 32,78,79,80,81,82,83,84,85 we use a new exact identity, 7,11,81 relating the one-particle and many-particle Green functions. Using this identity, it was possible to formulate a consistent and general scheme for construction of generalized solutions of the Anderson model.…”

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

“…One should note that the BCS-Bogoliubov superconductivity theory [1,3,5,10,15] is formulated in terms of a trial (approximating) Hamiltonian H mod , which is a quadratic form with respect to the second-quantized creation and annihilation operators, including the terms responsible for anomalous (or non-diagonal) averages. For the single-band Hubbard model the BCS-Bogoliubov functional of generalized mean fields can be written in the following form [92,93,94,95]…”

Fundamental Principles of Theoretical Physics and Concepts of Quantum Protectorate and Emergence

“…We believe that all these concepts will serve for the future development of physics [17] as useful practical tools. Additional material and discussion of these problems can be found in recent publications [18,19].…”