Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice

Abstract

We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) N\'eel---valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled $C{P}^{2}$ models and we study its fixed point structure using a functional renormalization group approach in a suitable large $N$ limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the $C{P}^{N}$ model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.