We investigated the spin-$\frac{1}{2}$ Heisenberg model with competing ferromagnetic and antiferromagnetic interactions on diamond-decorated lattices. Tuning the exchange interactions to the boundary of the ferromagnetic phase, we analyze the models with two types of diamond units: distorted and ideal diamonds. In the distorted diamond model, flat bands in the magnon spectra indicate the localized states confined to small regions (trapping cells) of the lattice. Remarkably, these trapping cells can host up to five and seven localized states for square and cubic lattices, respectively, leading to macroscopic ground state degeneracy and high values of residual entropy. The problem of calculating ground state degeneracy reduces to that of noninteracting spins, whose spin value is equal to half the number of localized magnons in the trapping cell. In contrast, ideal diamond models feature ground states composed of randomly distributed isolated diamond diagonal singlets immersed in a ferromagnetic background. Counting the ground state degeneracies here maps onto the percolation problem in two- and three-dimensional lattices. Our analysis shows that ideal diamond models possess even greater ground state degeneracy than their distorted counterparts. These findings suggest that the synthesizing of diamond-decorated type compounds holds great promise for low-temperature cooling applications.
We investigated the spin-21 Heisenberg model with competing ferromagnetic and antiferromagnetic interactions on diamond-decorated lattices. Tuning the exchange interactions to the boundary of the ferromagnetic phase, we analyze the models with two types of diamond units: distorted and ideal diamonds. In the distorted diamond model, flat bands in the magnon spectra indicate the localized states confined to small regions (trapping cells) of the lattice. Remarkably, these trapping cells can host up to five and seven localized states for square and cubic lattices, respectively, leading to macroscopic ground state degeneracy and high values of residual entropy. The problem of calculating ground state degeneracy reduces to that of noninteracting spins, whose spin value is equal to half the number of localized magnons in the trapping cell. In contrast, ideal diamond models feature ground states composed of randomly distributed isolated diamond diagonal singlets immersed in a ferromagnetic background. Counting the ground state degeneracies here maps onto the percolation problem in two- and three-dimensional lattices. Our analysis shows that ideal diamond models possess even greater ground state degeneracy than their distorted counterparts. These findings suggest that the synthesizing of diamond-decorated type compounds holds great promise for low-temperature cooling applications.
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 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.
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 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=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.
We study the ground-state phase diagrams and properties of spin-1/2 Heisenberg models on the diamond-like-decorated square and triangular lattices. The diamond-like-decorated square (triangular) lattice is a lattice in which the bonds of a square (triangular) lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the strength of the diagonal bond to that of the other four edges determines the ground-state properties. In particular, the macroscopically degenerated tetramer-dimer states, which are equivalent to the dimer covering states of the original lattices, are stabilized for λc < λ < 2, where the value of λc depends on the lattices. To determine the phase diagrams and boundaries λc, we employ the modified spin wave (MSW) method and the quantum Monte Carlo (QMC) method to estimate the ground-state energies of the ferrimagnetic states for λ < λc, where we can consider the mixed spin-1 and spin-1/2 Lieb-lattice and triangular Lieb-lattice Heisenberg antiferromagnets instead, and obtain λc(square)=0.974 and λc(triangular)=0.988. We also calculate the long-range order (LRO) parameters using the MSW and QMC methods and find the scaling relations where the spin reductions of each sublattice are inversely proportional to the number of sublattice sites. We prove these scaling relations by applying an infinitesimal uniform magnetic field. Furthermore, by examining the calculation process in the MSW, we clarify the mathematical structure behind the scaling relations for the sublattice LROs.