Fermion-induced quantum criticality with two length scales in Dirac systems

TL;DR

This paper investigates a fermion-induced quantum critical point in two-dimensional Dirac semimetals, revealing a universal critical behavior with two divergent length scales due to symmetry breaking, using a functional RG approach.

Contribution

It introduces a functional RG analysis of fermion-induced quantum criticality in Dirac systems, highlighting the emergence of two length scales and detailed fixed point structure across dimensions.

Findings

Identification of a fermion-induced quantum critical point in Dirac systems.

Discovery of two divergent length scales due to symmetry breaking.

Analysis of the fixed point structure across different dimensions.

Abstract

The quantum phase transition to a $\mathbb{Z}_3$-ordered Kekul\'e valence bond solid in two-dimensional Dirac semimetals is governed by a fermion-induced quantum critical point, which renders the putatively discontinuous transition continuous. We study the resulting universal critical behavior in terms of a functional RG approach, which gives access to the scaling behavior on the symmetry-broken side of the phase transition, for general dimension and number of Dirac fermions. In particular, we investigate the emergence of the fermion-induced quantum critical point for space-time dimensions $2<d<4$. We determine the integrated RG flow from the Dirac semi-metal to the symmetry-broken regime and analyze the underlying fixed point structure. We show that the fermion-induced criticality leads to a scaling form with two divergent length scales, due to the breaking of the discrete $\mathbb{Z}_3$ symmetry. This provides another source of scaling corrections, besides the one stemming from being in the proximity to the first order transition.