Frustrated spin models on two- and three-dimensional decorated lattices with high residual entropy

Abstract

We study the ground-state properties of a family of frustrated spin-1/2 Heisenberg models on two- and three-dimensional decorated lattices composed of connected star-shaped units. Each star is built from edge-sharing triangles with an antiferromagnetic interaction on the shared side and ferromagnetic interactions on the others. At a critical coupling ratio, the ideal star model - defined by equal ferromagnetic interactions - exhibits a macroscopically degenerate ground state, which we map onto a site percolation problem on the Lieb lattice. This mapping enables the calculation of exponential ground-state degeneracy and the corresponding residual entropy for square, triangular, honeycomb, and cubic lattices. Remarkably, the residual entropy remains high for all studied lattices, exceeding 60\% of the maximal value ln(2). Despite a gapless quadratic one-magnon spectrum, the low-temperature thermodynamics is governed by exponentially numerous gapped excitations. For a distorted-star variant of the model, the ground-state manifold is equivalent to that of decoupled ferromagnetic clusters, leading to exponential degeneracy with a lower, yet still substantial, residual entropy. At low temperature the system mimics a paramagnetic crystal of non-interacting spins with high spin value ($s=4$ for a square lattice). The obtained results establish a structural design principle for engineering quantum magnets with a high ground-state degeneracy, suggesting promising candidates for enhanced magnetocaloric cooling and quantum thermal machines.

Figures (12)

• Figure 1: Two versions of the extension of the diamond chain (shaded) to the square lattice: a) the diamond-decorated square lattice, and b) the square lattice formed by connected stars.
• Figure 2: An elementary cell (star) for the square lattice.
• Figure 3: Mapping of the model to a square Lieb lattice. Sites host composite spins $\mathbf{L}_{\mathbf{i}}$; bonds host monomer spins-$\frac{1}{2}$, $\mathbf{s}_{\mathbf{i},\mathbf{j}}$.
• Figure 4: A 4x4 Lieb lattice with a specific configuration of singlet sites (open circles, $L_i=0$). Shaded regions denote the resulting ferromagnetic clusters.
• Figure 5: Contributions to partition function $\ln W(K,N)$ (Eq.(\ref{['ZK']})) as a function of the connected-site fraction $p=K/N$ and different system sizes $N$ and lattices: (a) square; (b) triangular; (c) hexagonal; (d) cubic. Vertical red lines indicate the corresponding site-percolation thresholds.