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)

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.