Volume 81, Issue 4 - Special Issue: Frustrated spin systems and numerical methods; Guest Editors: Andreas Honecker and Jürgen Schnack

We present a comprehensive and rigorous analysis of the lowest energy configurations (LECs) of classical spin polygons characterized by arbitrary couplings between neighboring spin sites. Our study shows that these ground states exhibit either collinear or coplanar arrangements, which allows us to determine the precise boundaries between these two phases. By simultaneously applying a spin flip and a bond inversion, we simplify the LEC problem and reduce it to a specific scenario with predominantly ferromagnetic (FM) bonds and a single antiferromagnetic (AFM) bond. Hence, competing interactions are always present, but, nevertheless, in the well-defined ranges of the system parameters, the collinear LEC is realized. The difference angles between neighboring spins within the LEC can be captured by a single Lagrange parameter. We analytically investigate its dependence on the AFM bond and arrive at revealing results. Similarly, we can analyze the energy of the LEC, which shows a pronounced maximum as a function of the AFM bond. To illustrate our findings, we give various examples that clearly demonstrate these results.

The present view of modern physics on non-equilibrium dynamics is that generic systems equilibrate or thermalize under rather general conditions, even closed systems under unitary time evolution. The investigation of exceptions thus not only appears attractive, in view of quantum computing where thermalization is a threat it also seems to be necessary. Here, we present aspects of the one-magnon dynamics on the Kagome lattice antiferromagnet as an example of a non-equilibrating dynamics due to flat bands. Similar to the one-dimensional delta chain localized eigenstates also called localized magnons lead to disorder-free localization and prevent the system from equilibration.

The ground state of the classical antiferromagnetic XX model in a magnetic field is calculated for spins mounted on the vertices of the icosahedron. The magnetization is characterized by two discontinuities as a function of the external field. For a wide field range above the first discontinuity the ground state is degenerate, with two spins related by spatial inversion almost aligned with the field and the rest forming two magnetization units in the form of pentagons. It is shown that the degeneracy originates from the coupling of the two pentagons, which introduces the triangle, associated with ground-state degeneracy, as an interaction unit in the icosahedron. The magnetization discontinuities are shown to evolve first from the coupling of isolated triangles and then from the addition of the two spins related by spatial inversion.

We investigate flat magnonic bands in a generalized sawtooth-chain model in which three sets of exchange parameters (symmetric Heisenberg exchange, axial Ising anisotropy, and antisymmetric Dzyaloshinskii–Moriya (DM) exchange) are assigned independently to each side of the triangular plaquette. If the effective Dzyaloshinskii–Moriya (DM) interaction parameters are generated via the Katsura–Nagaosa–Balatsky (KNB) mechanism of magnetoelectricity, they become explicit functions of the electric-field magnitude and direction, as well as of the lattice geometry, which in the present case is characterized by two bond angles. We focus on the situation in which these two angles are unequal, corresponding to a distortion of the triangular plaquette. Several electric-field–induced flat-band scenarios in the distorted sawtooth chain are analyzed, and expressions are derived for the electric-field strength required to drive the one-magnon excitations into a flat-band regime when the field is aligned along the lattice bonds. The saturation field and its dependence on the distortion angle are also examined. Finally, we establish a mapping between the flat-band solutions for a general DM interaction and its specific KNB-induced form.

We present a systematic study of multi-magnon bound states (MBSs) in the spin- 1 2 $\frac{1}{2}$ FM-AFM J 1 - J 2 chain under magnetic fields using the density-matrix renormalization group method. As a quantitative measure of stability, we compute the magnon binding energy E b ( M , p ) for bound clusters of size p over wide ranges of the frustration ratio J 2 /| J 1 | and the normalized magnetization M / M s . Near saturation, we benchmark our data against the analytic two-magnon result and map out a clear hierarchy of p -magnon states, whose phase boundaries follow an empirical scaling J 2,c ( p ;  p + 1)/| J 1 | ≈ 0.34 p −2.3 for large p . We further quantify the relation between the most stable p and the zero-field pitch angle θ , verifying the conjectured inequality 1/ p > θ / π > 1/( p + 1) up to p ≲ 9. The binding energy shows pronounced suppression as J 2 /| J 1 | → 1/4 + and, for some frustration values, attains a maximum below full saturation, indicating that partial depolarization enhances bound-magnon mobility. Close to the FM instability, E b ( M s , p ) exhibits an empirical power-law vanishing consistent with a quantum-Lifshitz scenario. Our results provide a comprehensive, experimentally relevant map of MBS stability across field and frustration, offering concrete guidance for inelastic probes in quasi-one-dimensional magnets.

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 antiferromagnet on a distorted diamond-decorated honeycomb lattice in an external magnetic field. By combining density-matrix renormalization group, sign-problem-free quantum Monte Carlo in a mixed dimer–monomer basis, exact diagonalization, and an effective lattice-gas approach, we determine the ground-state phase diagram and analyze the finite-temperature magnetization process. The model hosts a rich variety of frustration-induced quantum phases including a quantum ferrimagnetic phase of Lieb–Mattis type, a quantum ferromagnetic phase, a spin-canted phase, a monomer–dimer phase, a dimer–tetramer liquid, a dimer-tetramer solid, and two distinct one-dimensional-crossover phases of ferromagnetic and ferrimagnetic character. Depending on the lattice distortion, we identify robust magnetization plateaus at 0, 1/4, 1/2, and 3/4 of the saturation magnetization originating from competing local dimer and tetramer singlets. Finite-temperature QMC data reveal how thermal fluctuations progressively smear the plateau structure, while the effective lattice-gas description reliably captures the corresponding low-temperature behavior.