Deconfined Quantum Critical Point on the Triangular Lattice

TL;DR

This paper proposes a topological term and demonstrates, through renormalization group analysis, the existence of a continuous deconfined quantum critical point between antiferromagnetic and valence bond solid orders on a triangular lattice, described by $N_f=4$ QED.

Contribution

It introduces a topological term capturing order intertwinement and establishes a controlled proof of a deconfined quantum critical point with emergent symmetry on the triangular lattice.

Findings

Existence of a continuous dQCP between two ordered phases.

Description of the dQCP using $N_f=4$ QED with emergent PSU(4) symmetry.

Connection of the dQCP physics to the boundary of a 3D bosonic SPT state.

Abstract

We first propose a topological term that captures the "intertwinement" between the standard "$\sqrt{3} \times \sqrt{3}$" antiferromagnetic order (or the so-called 120$^\circ$ state) and the "$\sqrt{12}\times \sqrt{12}$" 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 $N_f = 4$ quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/$Z_4$ symmetry only at the critical point. The topological term aforementioned is also naturally derived from the $N_f = 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.