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.
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.
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 spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate. The degree of this degeneration is found analytically. It is shown that the residual entropy per spin is
s0=21ln2. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The corresponding thermodynamic quantities are calculated using full exact diagonalization of finite chains up to
N=22. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.
We consider a spin-[Formula: see text] kagome-like chain with competing ferro- and antiferromagnetic anisotropic exchange interactions. The ground state phase diagram of this model consists of the ferromagnetic and ferrimagnetic phases. We study the ground state and the low-temperature properties on the phase boundary between these phases. The ground state on this phase boundary is macroscopically degenerate and consists of localized magnon states. We calculate the ground state degeneracy and corresponding residual entropy. The spontaneous magnetization has a jump on the phase boundary confirming the first-order type of the phase transition. In the limit of a strong anisotropy, the spectrum of the low-energy excitations has multi-scale structure governing the peculiar features of the specific heat behavior.
Exactly solvable frustrated quantum spin models consisting of a diamond unit structure are presented. The ground states are characterized by tetramer-dimer states with a macroscopic degeneracy in a certain range of isotropic exchange interaction. The lower bound of the excitation gap is exactly calculated to be finite and the bulk entropy in the limit of zero temperature remains finite depending on the shape of the boundary of system. Residual entropy is in a range of 0~6.1% of the entropy at high temperature for hexagonal diamond lattice and 0~8.4% for square diamond lattice. These diamond lattices are generalized to any dimensions and it is likely to be synthesized experimentally.