The static and dynamic properties of an isotropic quadrupolar system are studied by the method of double-time Green's functions. Using symmetrized equations of motion, a Dyson equation for the single-particle Green's function is obtained. The self-energy is expressed in terms of three-particle Green's functions, which are determined using an effective Hamiltonian, with the exact commutation relations approximated by quasiboson ones. A detailed expression for the lifetime of the elementary excitations is obtained.
The static and dynamic properties of an isotropic quadrupolar system are studied by the method of double-time Green's functions. Using symmetrized equations of motion, a Dyson equation for the single-particle Green's function is obtained. The self-energy is expressed in terms of three-particle Green's functions, which are determined using an effective Hamiltonian, with the exact commutation relations approximated by quasiboson ones. A detailed expression for the lifetime of the elementary excitations is obtained.
Recently we proposed a multichannel Dyson equation, in which we coupled the one- and the three-body Green's functions, to model photoemission spectra. In this work we extend this concept to higher-order Green's functions and to other spectroscopies. We show the general structure of the equations and how one can systematically approximate the corresponding multichannel self-energy. As a particular case, we focus on the coupling of the two-body and the four-body Green's functions in the electron-hole channel to describe neutral excitations. This formulation allows for the description of important many-body effects, such as biexcitons, in a natural way. We illustrate our approach by applying it to a two-level model system, which, in a one-particle picture, exhibits single and double excitations. Our method can correctly describe both kinds of excitation, unlike standard approaches, and in good agreement with the exact results.
We present the multichannel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's function with the three-body Green's function. We demonstrate that, unlike methods using only the one-body Green's function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multichannel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's function with the three-body Green's function. We demonstrate that, unlike methods using only the one-body Green's function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multi-channel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.
In this paper we discuss some general properties of the one-particle Green's function, for nonuniform many-fermion systems and the associated single-particle interpretation of physical properties of such systems. We consider, in particular, the ground-state energy, the density of particles in the ground state, and the single-particle excitation spectrum. The investigation is restricted to the case of a static external field and a system at zero temperature. Various general approximation methods are studied starting from one in which the self-energy operator is replaced by an Hermitian and energy-independent operator.
This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers. In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of non-equilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in terms of the special two-particle Green's function which describes current correlation. The discussion yields specifically a fluctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A method for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green's function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional effects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green's functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.
We propose a self-consistent many body theory for the standard basis operator Green 's functicms and obtain an exact Lyson type matriz equation for the interacting mcmy levei systems. A zeroth order crpproximation, which neglects ali the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadvopolar system and the Hubbard model. In case of the anisotropic Heisenberg ferromagnet with both exchange and single -ion anisotropy the low-temperature renomnalization of the apin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin -1 easy plane ferromagnet, the criticai parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin -1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen's like deccupling schemes. Finally, the theory is applied to the studW of the single -particle excitation spectrum of the Hubbard model.