We show that the Kasteleyn transition, the abrupt proliferation of infinite strings of defects in classical dimer and related models, can also be relevant for frustrated 2D quantum magnets. This is explicitly demonstrated in a phase of the spin-$1/2$ Heisenberg diamond-decorated honeycomb lattice where a family of exact eigenstates built as products of dimer and plaquette singlets can be mapped onto the dimer coverings of the honeycomb lattice. The low-temperature properties of this phase are accurately described by an effective dimer model with anisotropic activities and a small, tunable density of monomers, leading to an arbitrarily sharp crossover version of the Kasteleyn transition. The generalization to other geometries and the possibility of realizing this model in organometallic compounds are briefly discussed.

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• Magnetism
• Phase transitions
• Specific heat
• 2-dimensional systems
• Antiferromagnets
• Quantum spin models
• Exact diagonalization
• Quantum Monte Carlo
• Tensor network methods
• Transfer matrix method