Detecting Topological Quantum Phase Transitions via the c-Function

Abstract

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 maximum at the quantum criticality and distinguishes with great accuracy the two separate zero temperature phases. We expect our proposal to be a general feature of quantum phase transitions and to be applicable beyond the holographic framework.