Approaching Kasteleyn transition in frustrated quantum Heisenberg antiferromagnets

TL;DR

The paper addresses realizing Kasteleyn-type criticality in SU(2) quantum magnets by studying a spin-1/2 Heisenberg antiferromagnet on a diamond-decorated honeycomb lattice, which maps to an effective dimer model with a tunable monomer density $n_M$. Using a combination of exact diagonalization, finite-temperature Lanczos, DMRG, sign-problem-free QMC, and tensor-network CTMRG methods, the authors validate an effective monomer-dimer description (both EDM and EMDM) and identify a dimer-tetramer phase whose low-energy manifold corresponds to honeycomb dimer coverings with a small entropy per spin. In the weakly distorted regime, they show that a sharp Kasteleyn-type crossover emerges at $T_K$ with $T_K = \delta/\ln 2$ (where $\delta = J_2' - J_2$) in the zero-monomer limit, while a finite monomer density rounds the transition into a crossover with a finite correlation length. The work provides a rare, tunable quantum platform linking frustrated magnetism to classical dimer criticality and suggests experimental realizations in organometallic compounds and related lattices, broadening the reach of Kasteleyn physics in quantum materials.

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 to realize this model in organo-metallic compounds are briefly discussed.

Figures (7)

• Figure 1: Upper panel: Ground-state phase diagram of the spin-$\tfrac{1}{2}$ Heisenberg antiferromagnet on the diamond-decorated honeycomb lattice in the $J_2$–$J_2'$ plane. Numbers in parentheses indicate the density of triplet dimers. The unit cell illustrates the definition of couplings $J_1$, $J_2$, and $J_2'$. Lower panel: Schematic illustrations of the various phases characterized in the main text.
• Figure 2: Specific heat per spin $c$ as a function of temperature for the spin-$\frac{1}{2}$ Heisenberg model on the diamond-decorated honeycomb lattice with $J_2' - J_2 = 0.02$. (a) ED+FTLM results for $N = 32$ spins for several values of $J_2$. (b) Comparison of ED+FTLM results with QMC data at $J_2 = 1.3$, $J_2' = 1.32$ for two distinct system sizes $N = 32$ and $N = 288$.
• Figure 3: Specific heat of the spin-$\frac{1}{2}$ Heisenberg model on the diamond-decorated honeycomb lattice with $J_2 = 1.3$, $J_2' = 1.32$. Comparison of ED+FTLM for $2 \times 2$ unit cells of the original model with EDM and EMDM for $2 \times 2$ and $\infty \times 10$ unit cells.
• Figure 4: (a) Specific heat $c$ and (b) correlation length $\xi$ for the spin-$\frac{1}{2}$ Heisenberg model on the diamond-decorated honeycomb lattice in the weakly distorted regime $J_2' - J_2 = 0.02$ as obtained from the EMDM using CTMRG in the thermodynamic limit for distinct values of $J_2$. Insets highlight the low-temperature regime around the Kasteleyn crossover: in panel (a) for the specific heat and in panel (b) for the monomer density $n_M$. In panel (a), the exact result for the specific heat of the EDM is also shown by a thin black line.
• Figure 5: Part of the diamond-decorated honeycomb lattice with the unit cell shown in the yellow rhombus. The intra-dimer couplings $J_2$ and $J_2'$ within vertical and zig-zag diamonds are shown as thick red and green lines, whereas the monomer-dimer couplings $J_1$ are depicted as thin blue lines.