Topological magnon bound-states in periodically modulated Heisenberg XXZ chains

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.

11 pages, 6 figures

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• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Topological bound states in interacting Su-Schrieffer-Heeger rings
• Topological magnetic excitations
• Radiative topological biphoton states in modulated qubit arrays
• Analytical solution of open crystalline linear 1D tight-binding models
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Simulation of two-boson bound states using arrays of driven-dissipative coupled linear optical resonators
• Doublons, topology and interactions in a one-dimensional lattice
• Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Topological pumping induced by spatiotemporal modulation of interaction
• Topological Surface-plasmon-polaritons on Corrugated Metal-dielectric Surfaces
• Decay rates and energies of free magnons and bound states in dissipative XXZ chains
• Emergent Non-Hermitian Edge Polarisation in an Hermitian Tight-binding Model
• Confinement and oscillating deconfinement crossover of two-magnon excitations in quantum spin chains quantified by spin entanglement entropy
• Scattering Theory of Chiral Edge Modes in Topological Magnon Insulators
• Topological bound states in a lattice of rings with nearest-neighbour interactions
• Correlated dynamics of three-particle bound states induced by emergent impurities in Bose-Hubbard model
• Topological two-particle dynamics in a periodically driven lattice model with on-site interactions
• Vortex bound states in dimerized $\pi$-flux optical lattices: characterization, state preparation and current measurement
• Tunable multi-magnon Floquet topological edge states