Continuous and discontinuous topological quantum phase transitions

TL;DR

This paper investigates the stability of the continuous topological quantum phase transition in three-dimensional insulators under electronic interactions, revealing conditions for transition alteration or elimination.

Contribution

It provides a detailed analysis of how short-range interactions affect the nature of topological phase transitions, including the emergence of first order transitions and intervening phases.

Findings

Weak interactions do not alter the transition

Strong interactions can induce first order transitions

Intervening axionic insulator phase can eliminate the transition

Abstract

The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd "axionic" insulator. We also demonstrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions.