The Structure of Operators in Effective Particle-Conserving Models

TL;DR

This paper analyzes the structure of effective Hamiltonians and observables in many-particle lattice systems, showing how basis transformations that conserve particle number simplify the understanding and calculation of n-particle irreducible quantities.

Contribution

It introduces a systematic perturbative approach to construct effective operators conserving particle number, enhancing the analysis of many-particle systems.

Findings

Effective operators provide an intuitive understanding of the system.

Systematic calculation of n-particle irreducible quantities is enabled.

The approach is applicable to a broad class of systems.

Abstract

For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians conserving the number of excitations. The same transformation must be used to obtain effective observables. The analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem. The systematic calculation of n-particle irreducible quantities becomes possible constituting a significant progress. Details how to implement the approach perturbatively for a large class of systems are presented.