Reply to “Comment on ‘Thermodynamics of quantum crystalline membranes’ ”

We reply to the preceding Comment by Kats and Lebedev [Phys. Rev. B 90, 176301 (2014)] about our paper [Phys. Rev. B 89, 224307 (2014)]. Kats and Lebedev criticize the validity of our calculation with the use of a Debye momentum as an ultraviolet regulator of the theory and the obtention of a $k^2$ term for the self-energy of out-of-plane modes. The arguments presented by Kats and Lebedev ignore basic facts about the theory of crystalline membranes. We address and counter argue the criticisms presented about our paper.