Evolution of two-magnon bound states in a higher-spin ferromagnetic chain with single-ion anisotropy: A complete solution

TL;DR

This paper provides an exact analytical solution for the evolution of two-magnon bound states in a higher-spin ferromagnetic chain with single-ion anisotropy, revealing parameter regions supporting various bound states and their phase diagram mappings.

Contribution

It introduces a complete analytical solution for two-magnon bound states in a higher-spin chain, clarifying their evolution and coexistence regions with a novel phase diagram approach.

Findings

Identification of parameter regions supporting different two-magnon bound states

Discovery of a narrow region with coexisting single-ion bound states

Mapping of bound state evolution to a rectilinear movement in phase diagrams

Abstract

Few-magnon bound states in quantum spin chains have been long studied and attracted much recent attentions. For a higher-spin ferromagnetic XXZ chain with single-ion anisotropy, several features regarding the evolution of the low-lying two-magnon bound states with varying wave number were observed in the literature. However, most of these observations are only qualitatively understood due to the lack of analytical tools. By combining a set of exact two-magnon Bloch states and a plane-wave ansatz, we achieve a complete solution of the two-magnon problem in such a system. We identify parameter regions that support different types of two-magnon bound states, with the boundaries defined by algebraic equations. We discover for the first time a narrow region in which two single-ion bound states coexist. We show that the phase diagrams for distinct wave numbers are similar to each other, which enables us to map the evolution of the bound states to the rectilinear movement of a representative point for given parameters in a rescaled phase diagram. This dynamic picture provides quantitative interpretations of the observed features.