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arXiv:2601.14382 · Physical Review Letters

Approaching Kasteleyn Transition in Frustrated Quantum Heisenberg Antiferromagnets

Anonymous, Afonso Rufino, Taras Verkholyak, Nils Caci, Stefan Weßel, Jozef Strečka, Frédéric Mila, A. Honecker

Published Aug 3, 2026• 0 citations
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Abstract

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.

DOI
10.1103/4cn4-fymq

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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.
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.
Abstract We investigate the spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice in an external magnetic field. By combining density-matrix renormalization group, sign-problem-free quantum Monte Carlo in a mixed dimer–monomer basis, exact diagonalization, and an effective lattice-gas approach, we determine the ground-state phase diagram and analyze the finite-temperature magnetization process. The model hosts a rich variety of frustration-induced quantum phases including a quantum ferrimagnetic phase of Lieb–Mattis type, a quantum ferromagnetic phase, a spin-canted phase, a monomer–dimer phase, a dimer–tetramer liquid, a dimer-tetramer solid, and two distinct one-dimensional-crossover phases of ferromagnetic and ferrimagnetic character. Depending on the lattice distortion, we identify robust magnetization plateaus at 0, 1/4, 1/2, and 3/4 of the saturation magnetization originating from competing local dimer and tetramer singlets. Finite-temperature QMC data reveal how thermal fluctuations progressively smear the plateau structure, while the effective lattice-gas description reliably captures the corresponding low-temperature behavior.
We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the diagonal bond strength to that of the other four edges controls the frustration strength. For 0.974 < λ < 2, the present system has a nontrivial macroscopic degeneracy, which is called the macroscopically degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the Hilbert space of the Rokhsar–Kivelson (RK) quantum dimer model (QDM). By introducing further neighbor couplings in the MDTD states, we calculate the second-order effective Hamiltonian, which is exactly the same as the square-lattice QDM with a finite hopping amplitude t and dimer-dimer interaction v. Furthermore, we calculate v/|t| as a function of the ratio λ in the Heisenberg model and examine which phases of the square-lattice QDM appear in our obtained states. Our obtained QDM has a region where λ exhibits a finite hopping amplitude (|t| > 0) and repulsive interaction between dimers (v > 0). This suggests the possibility of realizing the resonating valence bond (RVB) state because the RVB state is obtained at v = |t|, which is known as the RK point.
The spin-1/21/21/2 quantum Heisenberg model on the diamond-decorated honeycomb lattice in a magnetic field is investigated using complementary analytical and numerical methods. The ground-state phase diagram comprises Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, spin-canted, and saturated paramagnetic phases, giving rise to characteristic magnetization plateaus, continuous and discontinuous field-induced transitions. In the highly frustrated regime, a localized-magnon approach based on an effective classical lattice-gas model provides an accurate description of the low-temperature magnetism and thermodynamics in agreement with numerical results. At intermediate frustration, finite-temperature calculations reveal characteristic specific-heat signatures of the field-induced transitions including the development of Ising critical behavior at the field-induced transition between the monomer-dimer and Lieb-Mattis ferrimagnetic phase.
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.