We solve few-magnon problems for a finite-size spin-
S periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets of exact Bloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the absence of the single-ion anisotropy, we reveal the condition under which exact zero-energy states emerge. As applications of the formalism, we calculate the transverse dynamic structure factor for a higher-spin chain near saturation magnetization and find signatures of the multimagnon bound states. We also calculate the real-time three-magnon dynamics from certain localized states, which are relevant to cold-atom quantum simulations, by simulating single-particle quantum walks on the effective lattices. This provides a physically transparent interpretation of the observed dynamics in terms of propagation of bound state excitations. Our method can be directly applied to more general spin or itinerant particle systems possessing translational symmetry.
Few-magnon excitations in Heisenberg-like models play an important role in understanding magnetism and have long been studied by various approaches. However, the quantum dynamics of magnon excitations in a finite-size spin-
S XXZ chain with single-ion anisotropy remains unsolved. Here, we exactly solve the two-magnon (three-magnon) problem in the spin-
S XXZ chain by reducing the few-magnons to a fictitious single particle on a one-dimensional (two-dimensional) effective lattice. Such a mapping allows us to obtain both the static and dynamical properties of the model explicitly. The zero-energy-excitation states and various types of multimagnon bound states are manifested, with the latter being interpreted as edge states on the effective lattices. Moreover, we study the real-time multimagnon dynamics by simulating single-particle quantum walks on the effective lattices.
Quasi-one-dimensional materials serve as both testbeds for tractable magnetic models and as a perennial source of intriguing physics. An excellent example is the emergence of multimagnon bound states in ferromagnetic (FM) spin chains, which provide a platform for probing a few-body quantum phenomenon. Despite being studied for many years, the exchange anisotropy-driven bound state of a FM chain has yet to be observed by inelastic neutron scattering (INS). As INS provides a unique window into the nature of magnon-magnon interactions, this represents a substantive gap in the literature. Here, the authors rectify this gap by presenting detailed INS data on the
S=\textonehalf{} spin chain Li
2CuO
2. Their data allows for determination of a refined spin Hamiltonian which fully describes the one-magnon dispersion. With these details in hand, they demonstrate the existence of two-magnon and, potentially, three-magnon bound states in Li
2CuO
2, with the potential three-magnon bound state showing anomalous behavior.
The study of thermalization and its breakdown in isolated systems has led to a deeper understanding of nonequilibrium quantum states and their dependence on initial conditions. The role of initial conditions is prominently highlighted by the existence of quantum many-body scars, special athermal states with an underlying effective superspin structure, embedded in an otherwise chaotic many-body spectrum. Spin Heisenberg and
XXZ models and their variants in one and higher dimension have been shown to host exact quantum many-body scars, exhibiting perfect revivals of spin helix states that are realizable in synthetic and condensed matter systems. Motivated by these advances, we propose experimentally accessible, local, time-dependent protocols to explore the spatial thermalization profile and highlight how different parts of the system thermalize and affect the fate of the superspin. We identify distinct parametric regimes for the ferromagnetic (
X-polarized) initial state based on the interplay between the driven spin and the rest, including local athermal behavior where the driven spin effectively decouples, acting like a ``cold'' spot while being instrumental in heating up the other spins. We also identify parameter regimes where the superspin remains resilient to local driving for long timescales. We develop a real- and Floquet-space picture that explains our numerical observations, and make predictions that can be tested in various experimental setups.
NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.
This thesis investigates two-dimensional quantum antiferromagnets, with a focus on the spin-
21 antiferromagnetic easy-axis XXZ model on a square and a honeycomb lattice. Describing the excitations and interactions of magnons in these models is of substantial interest, as magnons are the fundamental quasiparticles and can thus explain experimental observations. Already for the paradigmatic antiferromagnetic spin-
21 Heisenberg model on the square lattice, high-energy features of the magnon dispersion are understood via strong magnon-magnon interactions. Besides that, interesting high-energy features were recently observed in the honeycomb lattice, including a possible decay of the single-magnon mode. The goal of this thesis is to obtain effective descriptions of the aforementioned systems that capture the relevant features of the magnon excitations and their interactions. To study these features, this thesis employs continuous similarity transformations (CSTs), which enables a systematic derivation of an effective quasiparticle picture via so-called flow equations. The approach enables decoupling different magnon sectors and thus for investigating ground-state properties, single-magnon excitations, and multi-magnon bound states. The magnon description is derived from the non-Hermitian Dyson-Maleev representation, which describes fluctuations around a long-range magnetically ordered ground state. The flow equations are set up in momentum space, truncated by the scaling dimension, retaining only operators up to scaling dimension of two, and solved numerically. For the square lattice, a magnon-conserving effective Hamiltonian is obtained across the full anisotropy range by interpolating between the Ising limit and the Heisenberg limit. The ground-state energy, staggered magnetization, dispersion, and critical exponents are in excellent agreement with the literature, supporting the validity of CST also for gapped phases. Two-magnon excitations in the
Sz=0 subspace comprise four bound states, which are tracked across the anisotropy range. Their successive decay into the two-magnon continuum is determined by using the inverse participation ratio. For the honeycomb lattice, the magnon-conserving CST is reliable only up to
λ≲0.57; an adapted CST scheme that decouples only the ground state while preserving couplings between different higher-magnon sectors yields effective descriptions for all
λ and confirms stable long-range order. The low-energy properties determined in this way match the literature values. However, in the Heisenberg limit, the adapted approach fails to capture high-energy features, such as the experimentally observed decay into the multi-particle continuum at corners of the Brillouin zone. A termination of the magnon-conserving flow equations at a finite flow parameter before the divergence reveals a single-magnon decay at high energies, which is connected to a crossing of a two-magnon bound state with the single-magnon mode. The observed energy dip qualitatively agrees with Quantum Monte Carlo results, but magnon–magnon interactions are overestimated, hindering a fully quantitative characterization of the single-magnon dispersion. Analyzing multi-magnon bound states over the anisotropy range unveils that the crossing of a three-magnon bound state with the single-magnon mode accounts for the breakdown of the magnon-conserving CST at higher
λ. This work demonstrates that CST with scaling-dimension truncation provides a powerful framework for studying two-dimensional quantum magnets, capturing low-energy properties and bound states. Nevertheless, challenges remain in accurately describing high-energy features arising from a persistent overlap of magnon sectors due to strong binding effects.