Confinement-deconfinement transitions in the dimer-loop models on two-dimensional non-bipartite lattices

Recent work [Kundu, Damle, Phys. Rev. X 15, 011018 (2025)] has demonstrated that a class of S=1 kagome lattice antiferromagnets with competing anisotropies can exhibit unusual low-temperature behavior that is best described in terms of the statistical mechanics of an interesting interpolation between the fully-packed dimer model and the fully-packed loop model on the bipartite honeycomb lattice. On this and other bipartite lattices in two and three dimension, such fully-packed dimer-loop models generically have two distinct power-law correlated Coulomb phases, both of which admit a low-energy description in terms of a fluctuating divergence-free polarization vector field [Phys. Rev. X 15, 011018 (2025); arXiv:2510.11607]. The transition between these phases corresponds to a confinement transition for the Z 2 part of the corresponding U(1) flux [Phys. Rev. X 15, 011018 (2025); arXiv:2510.11607]. Here we demonstrate that a variant of such a topological confinement transition can also exist in dimer-loop models on non-bipartite lattices such as the kagome and triangular lattices although the low-energy description does not feature any conserved U(1) flux. In these non-bipartite dimer-loop models, both phases are short-range correlated liquids, and the topological distinction between them is in terms of a Z 2-valued winding number instead of the flux of a divergence-free polarization field. In spite of this key difference, this transition appears to be in the same Ising universality class as the analogous transition of the bipartite dimer-loop models. These kagome and triangular lattice dimer-loop models correspond respectively to the low-energy limit of a class of S=1 antiferromagnets with competing anisotropies on the ruby lattice comprising a corner-sharing arrangement of fully-frustrated squares and a lattice of corner-sharing fully-frustrated hexagons.