Deconfined quantum criticality in two-dimensional bipartite SU(N) anti-ferromagnets

I will give an overview of unbiased numerical work on the N\'eel- valence bond solid (VBS) phase transition in $d=2$ anti-ferromagnets. This progress has been possible due to the discovery of a new class of Hamiltonians of SU($N$) spins that are free of the sign problem of quantum Monte Carlo. I will show through extensive numerical studies of the quantum phase transition on a variety of bipartite systems: square, rectangular, honeycomb and square bilayer, for a number of values of $N$ ($2 \leq N \leq 10$), that a close to complete picture of an unusual ``deconfined critical point'' has emerged. Significantly, no direct evidence for first order behavior has been found on the largest simulations with $256\times 256$ spins, the crucial role of Berry phases at the critical point has been verified, strong evidence for non-compact CP$^{N-1}$ universality is evident for a range of $N$ values, the inferred ``dangerous'' (ir)relevance of lattice anisotropy at the critical point is consistent with various limiting analytic calculations on the CP$^{N-1}$ field theory and close to the critical point dramatic signatures of the emergent photon excitation have been detected in VBS correlation functions. I will conclude with some open theoretical issues that remain to be resolved and possible experimental realizations.