From quantum dimers to the π -flux toric code via deconfined multicriticality

Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularization of the dimer Hilbert space that yields a qubit Hamiltonian interpolating from the RK model to the π -flux toric code, thereby accessing a deconfined Z 2 topological liquid. In this framework, the Z 2 liquid descends from a multicritical U ( 1 ) spin liquid through condensation of a charge-2 Higgs field, thus avoiding confinement. Using iDMRG together with low-energy field theory, we determine a phase diagram containing two continuous quantum phase transitions—a 3 D XY * transition between the Z 2 liquid and the columnar/plaquette-VBS, and a quantum Lifshitz transition between two dimer crystals—alongside a first-order transition between the staggered crystal and the Z 2 liquid. Our field theory suggests a deconfined multicritical point described by an Abelian Higgs model with dynamical critical exponent, z = 2 , where the three transitions meet, highlighting the interplay of fractionalization and emergent gauge fluctuations.