Determine whether the AFM–VBS transition is genuinely continuous or weakly first order

Determine whether the direct antiferromagnetic–valence-bond-solid transition in the compact lattice QED$_{2+1}$ model coupled to bond phonons is a continuous deconfined quantum critical point or a weakly first-order transition by analyzing larger system sizes.

Background

The simulations find no resolved intermediate phase or coexistence regime between AFM and VBS order, and the data show features associated with deconfined quantum criticality, including approximate emergent U(1) symmetry in the VBS order parameter and simultaneous softening of spin and dimer excitations.

However, the accessible finite-size data do not conclusively distinguish a continuous transition from a weakly first-order one. Larger-scale simulations are therefore required to establish the order and universality class of the direct AFM–VBS transition.

References

Even though the data does not show any clear evidence of a strong first-order transition, a weak first-order transition cannot be excluded without simulations at larger sizes.

— Unconstrained compact lattice QED$_{2+1}$ coupled to phonons: Gauss sectors, orthogonal semimetal, and deconfined criticality  (2609.20502 - Inácio et al., 17 Sep 2026) in Section 4.4, “AFM-VBS transition”