Deconfined Quantum Critical Point on the Triangular Lattice

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.

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• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
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• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Ferromagnetism and Spin-Valley liquid states in Moiré Correlated Insulators
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Building models of topological quantum criticality from pivot Hamiltonians
• Spin-Peierls instability of the U(1) Dirac spin liquid
• Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
• Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model
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• Magnetic field-driven transition between valence bond solid and antiferromagnetic order in distorted triangular lattice
• Spin-Peierls instability of deconfined quantum critical points
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Deconfined Quantum Critical Point with Non-locality
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Non-Landau Quantum Phase Transitions and nearly-Marginal non-Fermi Liquid