Perturbative Methods in Many-Body Problems

Philippe A. Martin, FRANÇOIS ROTHEN

Decio Levi B, O. Ragnisco

Manuel Valiente

Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension.

BRUCE R. BARRETT

A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei.

Reiner M. Dreizler, Eberhard K. U. Gross

Johannes T. Margraf, Rodney J. Bartlett

The study of systems with fractional charges and spins has become an extremely important tool to understand errors in approximate electronic structure methods, particularly in the context of density functional theory. Meanwhile, similar studies with wavefunction (WF)-based methods beyond second-order perturbation theory have been lacking. In this contribution, we study the performance of different coupled cluster (CC) and many-body perturbation theory (MBPT)-based methods for fractional charges. The use of the conventional and renormalized formulations of fractional-charge MBPT is discussed. The fractional spin behavior of the coupled cluster doubles (CCD) method is also investigated. Overall, all tested WF methods show very promising performance for the fractional charge problem. CCD is also quite accurate for the fractional spin problem in He+ across most of the range, although it breaks down to near Hartree-Fock quality in the strongly correlated limit. Beyond the study of fractional charge and spin curves, the implementation of CC methods with fractional occupation numbers offers a promising route to treating problems with multi-reference character in a single-reference framework.