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 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.

v2: matching the published version in PRD

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• Momentum relaxation in a holographic Weyl semimetal
• The mixed-state entanglement in holographic p-wave superconductor model
• Momentum relaxation of holographic Weyl semimetal from massive gravity
• Inverted c-functions in thermal states
• Holographic Lifshitz flows
• What's inside a hairy black hole in massive gravity?
• Diagnosing quantum phase transition via holographic entanglement entropy at finite temperature
• Nonequilibrium steady states in driven holographic Weyl semi-metals