  In this Reply, we respond to the comments in Phys. Rev. Lett. 130, 219702
(2023) on our Phys. Rev. Lett. 127, 176601 (2021) ''Coulomb instabilities of a
three-Dimensional higher-order topological insulator". We show the surface gap
given in Phys. Rev. Lett. 130, 219701 (2023) is different from the expression
derived by using the well-accepted approach and becomes divergent and singular
at lower energies, thus is not suitable for depicting the phase transition from
the 2nd-order to 1st-order topological insulator. We further show that a
correct surface gap can describe the phase transition if the RG scheme treats
the bulk gap as starting point. We justify our criteria in Phys. Rev. Lett.
127, 176601 (2021) for both the transitions from 2nd-order topological
insulator to 1st-order topological insulator and normal insulator.
