Tunable deconfined quantum criticality and interplay of different valence-bond solid phases

We use quantum Monte Carlo simulations to study an S=1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS-AFM and AFM-cVBS boundaries merge into a direct sVBS-cVBS transition. Unlike previous models with putative deconfined AFM-cVBS transitions, e.g., the standard J-Q model, in our extended J-Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z₄ symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order, the clock-like Z₄ fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.