Deconfined Quantum Critical Point on the Triangular Lattice

We first propose a topological term that captures the "intertwinement" between the standard antiferromagnetic order (or the so-called 120 degree state) and the valence solid bond (VBS) order for spin-1/2 systems on a triangular lattice. Then using a controlled renormalization group calculation, we demonstrate that there exists an unfine-tuned direct continuous deconfined quantum critical point (dQCP) between the two ordered phases mentioned above. This dQCP is described by the Nf=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4 symmetry only at the critical point. The topological term aforementioned is also naturally derived from the Nf=4 QED. We also point out that physics around this dQCP is analogous to the boundary of a 3d bosonic symmetry protected topological state with on-site symmetries only.