Compatible orders and fermion-induced emergent symmetry in Dirac systems

TL;DR

This paper demonstrates that in 2+1D Dirac systems, a stable multicritical point with emergent O(N1+N2) symmetry exists, enabling continuous phase transitions between different ordered phases, influenced by fermionic degrees of freedom.

Contribution

It establishes the existence of a stable RG fixed point with emergent symmetry at the multicritical point in Dirac systems, extending understanding of phase transitions with fermions.

Findings

Existence of a stable fixed point with emergent O(N1+N2) symmetry.

Irrelevance of small O(N)-breaking perturbations near the fixed point.

Predictions for critical behavior of chiral O(N) universality classes.

Abstract

We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with $O(N_1)$ and $O(N_2)$ symmetry, respectively. Using $\epsilon$ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent $O(N_1+N_2)$ symmetry for arbitrary values of $N_1$ and $N_2$ and fermion flavor numbers $N_f$, as long as the corresponding representation of the Clifford algebra exists. Small $O(N)$-breaking perturbations near the chiral $O(N)$ fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic $O(N)$ fixed point, which is stable only when $N < 3$. As a by-product, we obtain predictions for the critical behavior of the chiral $O(N)$ universality classes for arbitrary $N$ and fermion flavor number $N_f$. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.