Detecting Topological Quantum Phase Transitions via the c-Function

TL;DR

This paper introduces the c-function as an effective tool for detecting topological quantum phase transitions, demonstrated through a holographic model showing a transition between trivial insulator and Weyl semimetal phases.

Contribution

The paper proposes the c-function as a novel and accurate probe for topological quantum critical points, extending its potential applicability beyond holographic models.

Findings

The c-function accurately identifies the quantum critical point.

It distinguishes between trivial and topological phases with high precision.

The approach is conjectured to be broadly applicable to various quantum phase transitions.

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.