Kasteleyn Transition Achieved in Spin-1/2 Heisenberg Antiferromagnets with Dimer Singlets

Scientists are increasingly interested in understanding how complex magnetic behaviour emerges in frustrated quantum systems, and new research published details a surprising connection to classical dimer models. Katarina Karlova, Afonso Rufino (Institute of Physics, EPFL), Taras Verkholyak et al. demonstrate that the Kasteleyn transition , typically observed in arrangements of dimers , can also occur in the spin-1/2 Heisenberg diamond-decorated honeycomb lattice. By mapping exact magnetic eigenstates onto dimer coverings, the team reveal a pathway to an exceptionally sharp crossover resembling the Kasteleyn transition, offering a novel perspective on low-temperature magnetic properties and potentially opening doors to designing new organo-metallic compounds with tailored magnetic characteristics.

The team achieved a precise mapping between the quantum magnetic system and a classical dimer model, allowing for the application of well-established dimer model techniques to understand the magnetic material’s properties. This monomer density is key, as it allows for a tuning of the system towards a sharper crossover, mimicking the behaviour expected at a true Kasteleyn transition, even though a genuine transition is precluded by theoretical constraints. The study unveils a pathway to explore Kasteleyn-type criticality in a system governed by SU(2) symmetry, which typically forbids conventional finite-temperature critical behaviour.

These methods allowed for a comprehensive analysis of both the ground state and the thermodynamic properties of the system, confirming the validity of the effective dimer model description. The work opens possibilities for realizing this model in organo-metallic compounds, potentially leading to the experimental observation of these intriguing quantum phenomena. The study establishes that the observed crossover can be made arbitrarily sharp by tuning the monomer density to an extremely small value, effectively shifting the transition towards lower temperatures. This provides an example of emergent Kasteleyn-type criticality, offering a remarkable platform to investigate the interplay between monomers and the Kasteleyn transition. Furthermore, the research highlights the potential for synthesizing structural analogues of existing organo-metallic compounds, such as {Cu(bipn)}3Fe(CN)62 · 4H2O and [{Cu(ept)}3Fe(CN)6] (ClO4)2 ·5H2O, to experimentally realize the magnetic structure of the diamond-decorated honeycomb lattice and directly observe the predicted behaviour, This innovative approach promises to advance our understanding of frustrated magnetism and pave the way for novel quantum materials.

Dimer Mapping Reveals Kasteleyn Transitions in Magnets and

To comprehensively analyze both ground-state and thermodynamic properties, the study combined several complementary computational methods. These calculations build upon previous work on square-lattice versions of the model and are further detailed in the Supplemental Material, ensuring a robust and well-documented methodology.

Figure 1 presents the ground-state phase diagram obtained using the ALPS implementation of the density matrix renormalization group (DMRG) on a 4 × 4 unit-cell system containing 128 spins under periodic boundary conditions. The analysis first focused on the symmetric line defined by J₂ = J′₂. For J₂ = J′₂ < 2, a two-dimensional Lieb–Mattis (LM) phase was identified. As J₂ = J′₂ increased beyond this value, the system transitioned into a monomer–dimer (MD) phase characterized by singlet dimers separated by paramagnetic monomers.

Crucially, an intermediate regime, 0.95 ≲ J₂ = J′₂ ≲ 2, revealed a macroscopically degenerate dimer–tetramer (DT) phase composed of singlet tetramers and dimers. Additional insight into the undistorted case was obtained through exact diagonalization (ED) on a 32-site cluster containing 12 dimers and 8 monomeric sites. These calculations confirmed a triplet density of 1/3 within the DT phase and identified the lowest-energy excitations.

An analysis of the excitation gap, which reaches a maximum near J₂ ≈ 1.4, identified the most stable region of the DT phase and a suitable parameter regime for mapping the system onto an effective dimer model. Thermodynamic properties were further examined through specific heat calculations, shown in Figure 2, using a combination of ED with the finite-temperature Lanczos method (FTLM) and quantum Monte Carlo (QMC) simulations. System sizes of N = 32 and N = 288 were employed to validate the results and assess finite-size effects.

Three Peaks Reveal Magnet’s Low-Temperature Phases, confirming theoretical

The team measured specific heat per spin, revealing three distinct peaks at well-separated temperatures for various values of (J_2) and fixed (J’_2 – J_2 = 0.02). These measurements were conducted using exact diagonalization (ED) combined with finite-size scaling techniques (FTLM), providing a detailed description of the low-temperature phase behavior. The specific heat data, shown in Figure 0.2(a), demonstrated three peaks at temperatures (T \approx 0.02), (0.1), and (0.7). To validate these findings, the researchers compared their ED+FTLM results with quantum Monte Carlo (QMC) simulations for a system size of (N = 32) spins.

The agreement between the two methods was excellent in the accessible temperature range, particularly confirming the presence of the broad intermediate peak. The low-temperature peak, specifically at (T \approx 0.02), was attributed to the lifting of degeneracy in the ground-state manifold due to the difference between (J_2) and (J’_2). The specific heat data for this model, shown in Figure 0.3, confirmed that the low-temperature peak was dominated by ground-state configurations of the dimer-tetramer solid phase. Further analysis using the Corner Transfer Matrix Renormalization Group (CTMRG) technique revealed a sharp low-temperature peak associated with dimer physics, followed by a broader maximum due to monomer excitations. These results demonstrate the Kasteleyn transition in a weakly distorted version of the model, providing new insights into the interplay between dimer and monomer excitations in frustrated magnets. The breakthrough delivers a precise understanding of the low-temperature phase behavior and opens up possibilities for realizing similar models in organo-metallic compounds.

Dimer-Magnet Mapping Reveals Kasteleyn Transition Control in Stripe

The study establishes that tuning the interactions between spins (J′2, J2) can reduce the monomer density, bringing the system closer to a true Kasteleyn critical point, a rare and tunable quantum platform for emergent classical criticality. This work bridges quantum magnetism with the statistical mechanics of classical dimer models, potentially opening new avenues for exploring topologically and geometrically constrained phases in frustrated quantum spin systems. The authors acknowledge that while the model exhibits macroscopic ground-state degeneracy at a classical level, experimental systems are expected to lift this degeneracy, potentially through lattice distortions.