Abstract We study the ground state properties of the anisotropic spin-1/2 Heisenberg model on lattices built from ideal diamond units with competing ferro- and antiferromagnetic interactions. The study covers the one-dimensional diamond chain and its two- and three-dimensional generalizations. The ground-state phase diagram contains four distinct phases: ferromagnetic (F), critical (C), monomer-dimer (MD), and tetramer-dimer (TD), which converge at a quadruple point. We demonstrate the presence of macroscopic ground-state degeneracy and corresponding residual entropy, which is maximal at the quadruple point and also extends throughout the MD phase and its boundaries with TD and F phases. For the diamond chain, we derive exact degeneracies, while for higher-dimensional lattices, we map the problem onto a bond percolation model or used transfer-matrix approach, enabling the numerical computation of the ground state degeneracy.
We investigate the ground state properties, magnetization, and low-temperature thermodynamics of the ferromagnetic-antiferromagnetic spin-
s model on diamond-decorated lattices with ideal diamond units, incorporating bilinear Heisenberg and higher-order exchange interactions between diagonal spins-
σ. Local conservation of the composite spin on each diamond diagonal enables exact analysis. For the pure Heisenberg case, the system undergoes a series of
2σ transitions between monomer-dimer (MD), ferrimagnetic (Ferri) and ferromagnetic (F) phases with different optimal composite spin values as the coupling ratio varies. In the presence of higher-order interactions, a multicritical point exists where the states with all possible values of composite spin are degenerate, leading to maximal ground state degeneracy. The case
s=σ=1 with bilinear and biquadratic interactions is studied in detail. Its phase diagram comprises three phases - F, Ferri and MD, which meet at a triple point. On the phase boundaries, the ground state becomes macroscopically degenerate. For the diamond chain, we calculate the ground state degeneracy exactly; for higher dimensions, the problem maps onto a bond percolation framework, solved numerically. The residual entropy per spin reaches up to
60% of the maximal value, peaking at the triple point. Low-temperature magnetization curves in external magnetic fields exhibit plateaus and jumps. The excitation spectrum is gapped in the MD phase, gapless in the F phase, and resembles that of the Lieb-Mattis ferrimagnet in the Ferri phase. The high residual entropy suggests potential applications in ultra-low-temperature cooling and quantum thermal machines.
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.
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=4for 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.
The spin-
21 Heisenberg diamond chain with ferro- and antiferromagnetic exchange interactions is studied. The phase boundary in the parametric space of these interactions is determined, where the transition between the ferromagnetic and other (singlet or ferrimagnetic) ground state phases occurs. On this phase boundary there is a dispersionless (flat) energy band in the one-magnon spectrum and these states can be represented as localized magnons in the trapping cells between neighboring diamonds. The ground state consists of the localized magnons and special magnon complexes and it is macroscopically degenerate. A remarkable feature of the model is the existence, on a certain part of the phase boundary, of two- and three-magnon localized states, forming flat bands in two- and three-magnon spectrum. All these localized states also belong to the ground state manifold, which turns out to be exactly the same as for the system of independent spins-
23. This implies a large macroscopic degeneracy of the ground state
4n (
n is number of diamonds in the chain) and a high residual entropy per spin
s0=32ln2.
We study the ground-state phase diagram of a Heisenberg model with spin
S=21 on a diamond-like decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio
λ between the length of the diagonal bond and that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn {\bf85}, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of $λ_{\rm c}