Topological magnon bound-states in periodically modulated Heisenberg XXZ chains

TL;DR

This paper investigates topological magnon bound-states in periodically modulated Heisenberg XXZ chains, revealing their topological properties and protected edge states, advancing understanding of strongly interacting topological quantum states.

Contribution

It introduces a topological invariant based on cotranslational symmetry for multi-magnon states, enabling characterization of their topological features in quantum Heisenberg chains.

Findings

Existence of topological protected edge bound-states.

Calculation of Chern numbers for two-magnon bound-states.

Identification of cotranslational symmetry as key to topological classification.

Abstract

Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multi-particle quantum states, which enables us to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and Chern numbers of the two-magnon bound-states and show the existence of topological protected edge bound-states. Our study not only opens a new prospect to pursue topological magnon bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.