Katarína Karľová
Institute of Physics, Pavol Jozef Šafárik University in Košice

We study emergent dimer physics in frustrated spin-1/2 Heisenberg models on diamond-decorated square and honeycomb lattices. In both lattice geometries, moderately strong frustration leads to a macroscopically degenerate dimer–tetramer ground state that can be mapped onto effective classical dimer model. For the square lattice, we focus on the thermodynamic consequences of this macroscopic degeneracy. The residual entropy in the dimer–tetramer phase gives rise to an enhanced and asymmetric magnetocaloric effect, where the system can be efficiently cooled down to absolute zero temperature during the adiabatic demagnetization. We further show that the nature of low-energy excitations depends sensitively on the underlying dimer arrangement: while columnar order supports local excitations, staggered configurations lead to non-local, string-like excitations. Motivated by this behavior, we turn to the honeycomb lattice, where an effective dimer description naturally connects to Kasteleyn physics. Upon introducing a small anisotropy, the system exhibits signatures of highly asymmetric Kasteleyn-type phase transition including the proliferation of nonlocal string excitations and a strongly enhanced specific heat. However, in the full quantum model, the presence of monomer defects prevents the realization of a true phase transition in agreement with Lieb’s theorem. Nevertheless, in the regime of low monomer density, the system closely approaches Kasteleyn behavior when the highly asymmetric Kasteleyn-type phase transition can be approached asymptotically arbitrarily closely. Our results demonstrate how macroscopic degeneracy, lattice geometry, and local constraints produce rich thermodynamic phenomena and bridge for the first time the physics of classical dimer models with a genuine quantum spin system