Fermion-induced quantum critical points in two-dimensional Dirac semimetals

TL;DR

This paper studies how fermions can induce continuous quantum critical points in two-dimensional Dirac semimetals with $Z_3$ order, revealing conditions for their occurrence and characterizing their critical behavior.

Contribution

It provides an RG analysis showing fermion-induced quantum critical points occur above a critical flavor number and establishes an exact lower bound for this critical number.

Findings

FIQCPs occur when the number of Dirac fermion flavors exceeds a critical value

Two length scales and different critical exponents are characteristic of FIQCPs

An exact lower bound for the critical flavor number is established as greater than 1/2

Abstract

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and $Z_3$-ordered phases (e.g. Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first-order. From large-$N$ renormalization group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nature Communications 8, 314 (2017)] occur when $N$ (the number of flavors of four-component Dirac fermions) is larger than a critical value $N_c$. Remarkably, from the knowledge of spacetime supersymmetry, we obtain an exact lower bound for $N_c$, i.e., $N_c>1/2$. (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., $\nu$$\neq$$\nu'$, by large-$N$ RG calculations. We further give a brief discussion on possible experimental realizations of FIQCPs.