Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality

TL;DR

This paper studies SO(2) and SO(3) tensorial Gross-Neveu-Yukawa theories, revealing a new critical fixed point for N=3 and analyzing universal critical properties relevant for fractionalized spin-orbital liquids.

Contribution

It identifies a novel critical fixed point in SO(3) tensorial theories and explores the role of sextic interactions in ground state selection, extending understanding of phase transitions in these models.

Findings

Discovered a new critical fixed point for N=3.

Computed universal critical exponents up to two-loop order.

Demonstrated equivalence of N=2 case to the chiral XY model.

Abstract

We investigate the relativistic SO(2)- and SO(3)-invariant Gross-Neveu-Yukawa field theories for real, rank-two, symmetric, traceless tensor order parameters coupled to $N_{\text{f}}$ flavors of two-component Dirac fermions. These field theories arise as an effective description of fractionalized spin-orbital liquids. The two theories are the simplest and special cases of the more general class of field theories with SO($N$) symmetric tensor order parameter coupled to Dirac fermions, in which the symmetry is low enough to allow only one, and not the usual two quartic self-interaction terms. Using two-loop renormalization group near the upper critical dimension, we demonstrate that the theory exhibits a new critical fixed point for $N=3$ and the concomitant continuous phase transition for any value of $N_{\text{f}}$. For $N=2$ the theory is equivalent to the chiral XY model. We discuss the crucial role of the symmetry-allowed sextic self-interactions in the selection of the ground state configuration in the case of SO(3). The universal quantities such as the the anomalous dimensions of order parameters and fermions, the correlation length exponent, and the mass gap ratio between order parameter and fermion masses are computed up to $\epsilon^{2}$ order.