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Bulletin of the American Physical Society

Quantum magnet with a helical bond order adjacent to deconfined quantum criticality

Jun Takahashi, Bowen Zhao, Anders W. Sandvik

Published Mar 17, 2021• 0 citations
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We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) N\'eel---valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled $C{P}^{2}$ models and we study its fixed point structure using a functional renormalization group approach in a suitable large $N$ limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the $C{P}^{N}$ model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.

arXiv:1703.01308•Physical review. B./Physical review. B•May 25, 2017•6 citations
The S=1/2 square-lattice J-Q model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model-a term projecting staggered singlets, as well as a modulation of the J terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point-the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.
We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) N\'eel---valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled CP2C{P}^{2}CP2 models and we study its fixed point structure using a functional renormalization group approach in a suitable large NNN limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the CPNC{P}^{N}CPN model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.