Comment on "Thermodynamics of quantum crystalline membranes"

B. Amorim et al., (B.Amorim, R.Roldan, E.Cappelluti, A.Fasolino, F.Guinea, M.I.Katsnelson, Phys. Rev. B, v. 89, 224307 (2014)) reported the theoretical investigation of quantum crystalline membranes. In this comment we dismiss validity of their calculations based on a “natural” estimation of the ultra-violet (UV) divergent contributions into correlation functions. We claim that such calculations may not be performed correctly within the long-scale theory.