Relevance of Deconfined-Criticality Action in the Light of the J-Q Spin Model*

We perform large scale Monte Carlo simulations to study critical flows of 2D spin-1/2 J-Q model and 3D SU(2) symmetric discrete NCCP$^1$ model, a.k.a. deconfined-critical-point (DCP) action. The flows of the J-Q model and the DCP action collapse in a significantly large region of system sizes (up to L$\sim 60-80$), implying that the DCP theory (in general) and the discrete NCCP$^1$ model (in particular) correctly capture mesoscopic physics of the competition between the antiferromagnetic and valence-bond orders in quantum spin systems. At larger sizes we observe significant deviations between the two flows which both demonstrate strong violations of scale invariance. Furthermore, while the Neel state is perfectly space-time symmetric, the competing phase shows significant deviations from this symmetry. Possible scenarios are outlined.