For a class of frustrated spin lattices including the Kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the Kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

The description of quantized collective excitations stands as a landmark in the quantum theory of condensed matter. A prominent example occurs in conventional magnets, which support bosonic magnons—quantized harmonic fluctuations of the ordered spins. In striking contrast is the recent discovery that strongly spin-orbital-coupled magnets, such as α-RuCl₃, may display a broad excitation continuum inconsistent with conventional magnons. Due to incomplete knowledge of the underlying interactions unraveling the nature of this continuum remains challenging. The most discussed explanation refers to a coherent continuum of fractional excitations analogous to the celebrated Kitaev spin liquid. Here, we present a more general scenario. We propose that the observed continuum represents incoherent excitations originating from strong magnetic anharmonicity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of α-RuCl₃ and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state.

In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single $\mathrm{XXZ}$ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of $N$ weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number $N$ of cylindrically coupled chains numerically. For $N=3\mathrm{}$ we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\overrightarrow{N}\infty$.

The magnetization process of the orthogonal-dimer antiferromagnet ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$ is investigated in high magnetic fields of up to 118 T. A $1/2$ plateau is clearly observed in the field range 84 to 108 T in addition to $1/8$, $1/4$, and $1/3$ plateaus at lower fields. Using a combination of state-of-the-art numerical simulations, the main features of the high-field magnetization, a $1/2$ plateau of width 24 T, a $1/3$ plateau of width 34 T, and no $2/5$ plateau, are shown to agree quantitatively with the Shastry-Sutherland model if the ratio of inter- to intradimer exchange interactions $J^{\prime }/J=0.63$. It is further predicted that the intermediate phase between the $1/3$ and $1/2$ plateaus is not uniform but consists of a $1/3$ supersolid followed by a $2/5$ supersolid and possibly a domain-wall phase, with a reentrance into the $1/3$ supersolid above the $1/2$ plateau.

Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagome lattices using exact diagonalization (ED) for up to N=40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagome lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.