Comment on the paper "Quasi-particle approach for lattice Hamiltonians with large coordination numbers" by P. Navez, F. Queisser and R. Sch\"utzhold - J. Phys. A: Math. Theor. 47 225004 (2014)

TL;DR

This comment critiques the convergence issues of the large coordination-number expansion in a specific quantum lattice model, emphasizing the importance of controllable methods for accurate physical interpretation.

Contribution

It highlights the non-analyticity and potential pitfalls of perturbation expansions in large coordination-number models, stressing the need for controllable approaches.

Findings

Perturbation expansions may be invalid due to non-analyticity.

Uncontrollable methods can mislead experimental interpretations.

Recent work analyzes convergence issues in cluster models.

Abstract

This comment regards a central aspect of the referred-to paper, the issue of convergence of the large coordination-number expansion. Perturbation expansions of expressions containing a large number of parameters are generally invalid due to the non-analyticity of the expanded expressions. I refer to recent work where these issues are analyzed and discussed in detail in relation to a benchmark example of a cluster model. As discussed therein, methods which are uncontrollable and for which their convergence is not foreseeable are not only useless but can mislead, particularly if models derived from them are used to interpret experiments.