A direct approach to the calculation of many-body Green' s functions: quasi-particles and more

Giovanna Lani, Pina Romaniello, Lucia Reining

M R Bhagavan

Ashok Chatterjee, Soma Mukhopadhyay

This chapter examines the energy of the resulting quasi-particle using the Green function technique. The field-theoretic Green function technique developed originally by Feynman, Dyson, and others for quantum electrodynamics finds extensive applications to the many body problems encountered in different branches of physics, for its proven efficacy in dealing with the dynamical effects associated with these problems. The Green function formalism is essentially a systematic time-dependent perturbation theory involving certain quantities called the Green functions or propagators. The energy-dependent Green function, G, provides great many physical information about a system, in particular the energy of the quasi-particles. Puff and Whitfield have considered the thermodynamic Green functions for the problem and found at the end of the calculation the zero-temperature limit. In the zero-temperature limit the approximate thermodynamic Green function of Mahan becomes equivalent to the intermediate coupling polaron model of Haeringen and is thus expected to give the same result as given by method of Haeringen.

Roger Balian, Lewis H. Nosanow, N. R. Werthamer

Min-Fong Yang

Understanding correlation effects in topological phases of matter is at the forefront of current research in condensed matter physics. Here we try to clarify some subtleties in studying topological behaviors of interacting Weyl semimetals. It is well known that there exist two topological invariants defined to identify their topological character. One is the many-body Chern number, which can be directly linked to the Hall conductivity and thus to the two-particle correlations. The other is the topological index constructed from the single-particle Green's functions. Because the information on Green's functions is achieved more easily than the many-body wave functions, usually only the topological index is employed in the literature. However, the approach based on the single-particle Green's function can break down in the strongly correlated phase. For illustration, an exactly solvable two-orbital model with momentum-local two-body interactions is discussed, in which both topological invariants can be calculated analytically. We find that the topological index calculated from the Green's function formalism can be nonzero even for a nontopological strongly correlated phase with a vanishing many-body Chern number. In addition, we stress that the physical surface states implied by nonzero many-body Chern numbers should be the edge modes of particle-hole collective excitations, rather than those of a quasiparticle nature derived from the Green's function formalism. Our observations thus demonstrate the limitation of the validity of the Green's function formalism in the investigations of interacting topological materials.

Shokichi Kanno

We apply the method of quasi-linear canonical transformation proposed in a previous paper to the system of N interacting bosons, and we calculate the excitation energy for the dilute hard-sphere Bose gas. In our formulation the total number of the particles are exactly conserved in contrast with the Bogoliubov theory. There appears no logarithmic divergent term in the physical quantities which correspond to the self-energy operators Σ11 and Σ02 appearing in the method of Green's function.