Generalized diagonalization scheme for many-particle systems

TL;DR

This paper introduces a versatile diagonalization scheme for many-particle Hamiltonians that unifies various transformation and perturbation methods within a single framework, enabling direct evaluation of physical quantities.

Contribution

It presents a novel generalized diagonalization method using projection operators, applicable to both perturbative and non-perturbative treatments of many-particle systems.

Findings

Unified framework for diagonalization and perturbation theory

Applicable to diverse many-particle problems

Allows direct evaluation of physical quantities

Abstract

Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians represent an important direction in the field. Among these techniques the method, presented here, might be that approach with the widest range of possible applications: We demonstrate that both stepwise and continuous unitary transformations to diagonalize the many-particle Hamiltonian as well as perturbation theory and also non-perturbative treatments can be understood within the same theoretical framework. The new method is based on the introduction of generalized projection operators and allows to develop a renormalization scheme which is used to evaluate directly the physical quantities of a many-particle system. The applicability of this approach is shown for two important elementary many-particle problems.