  We propose the c-function as a new and accurate probe to detect the location
of topological quantum critical points. As a direct application, we consider a
holographic model which exhibits a topological quantum phase transition between
a topologically trivial insulating phase and a gapless Weyl semimetal. The
quantum critical point displays a strong Lifshitz-like anisotropy in the
spatial directions and the quantum phase transition does not follow the
standard Landau paradigm. The c-function robustly shows a global feature at the
quantum criticality and distinguishes with great accuracy the two separate zero
temperature phases. Taking into account the relation of the c-function with the
entanglement entropy, we conjecture that our proposal is a general feature of
quantum phase transitions and that is applicable beyond the holographic
framework.
