Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain

Abstract

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 static and dynamical properties of the model explicitly. The zero-energy 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.Introduction.-The Heisenberg XXZ model is a paradigmatic model exhibiting strong correlations. On the one hand, dynamical properties of the spin-1/2 XXZ chain continue to attract the attention of the solid-statephysics community [1][2][3][4]. On the other hand, recent experimental advances in cold atom systems enable realizations of the XXZ chain and preparation of certain initial states [5, 6], even with higher spins [7], providing an ideal setting for studying nonequilibrium quantum dynamics. Recently, few-magnon dynamics in the spin-1/2 XXZ chain has also attracted great theoretical interest [8,9].

Multimagnon dynamics and thermalization in the $S=1$ easy-axis ferromagnetic chain

“…Finally, the study of bound states in higher spin chains may also be of interest, as has been recently studied in Ref. [62].…”