Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase

In this talk, we will discuss two deformations of S = 1/2 square-lattice J-Q model, which hosts deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states [1]. In the first case, we introduce a term projecting staggered local singlets, which preserves all symmetries of the square lattice. The second case is a modulation of the J terms forming alternating “staircases” of strong and weak couplings, but still preserves the four-fold degeneracy of the columnar valence bond solid states.
Using the method applied in [2], we calculate the scaling dimension of both cases and show that each case introduces a second relevant field. In particular, the “staircases” deformation leads to a helical valence-bond phase, and we can identify the deconfined quantum critical point as a multicritical Lifshitz point—the end point of the helical phase.

Reference:
[1] B. Zhao, J. Takahashi, and A. W. Sandvik, arXiv: 2005.10184 (2020).
[2] A. W. Sandvik and B. Zhao, Chinese Physics Letters 37 (5), 57502 (2020).