Deconfined quantum criticality in bipartite SU($N$) antiferromagnets in two dimensions

The theory of deconfined quantum criticality shatters the celebrated paradigm of the Landau-Ginzburg-Wilson description of phase transitions by allowing for direct, continuous, quantum phase transitions between conventional, ordered phases that spontaneously break fundamentally different symmetries of the system. In this talk, I will present new results of a quantum Monte Carlo study of a local, SU($N$) symmetric, antiferromagnetic spin model on the honeycomb and anisotropic rectangular lattices. In particular, I will show evidence for the existence of a continuous phase transition separating conventional N\'{e}el and valence bond solid ordered phases, as well as comparisons of the extracted critical exponents for sufficiently large values of $N$ to those calculated analytically via a $1/N$ expansion solution of the CP$^{N-1}$ gauge field theory that is believed to accurately describe the behavior at the critical point. In combination with previous results of a similar study on the square lattice, this allows for a robust understanding of how the existence of deconfined quantum criticality depends on the lattice symmetries as a function of $N$, and therefore gives a complete picture of the phenomenon in bipartite SU($N$) systems in two dimensions.