Bound state dynamics in the long-range spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> XXZ model

Experimental platforms based on trapped ions, cold molecules, and Rydberg atoms have made possible the investigation of highly-nonlocal spin-${1/2}$ Hamiltonians with long-range couplings. Here, we study effects such non-local couplings in XXZ Heisenberg Hamiltonian. We calculate explicitly two-spin energy spectrum, which describes all energetic configurations two spins pointing a specific direction embedded background opposite orientation. For fast decay spin-spin couplings, find that spectrum is characterized by well-defined discrete values, corresponding to bound states, separated set continuum states describing scattering region. In deep regime instead, disappear as they get incorporated The presence results be crucial determine both two- many-spin dynamics. On one hand, radically different spreadings can observed tuning spin other enable dynamical stabilization effective antiferromagnetic ferromagnetic Finally, propose novel scheme trapped-ion quantum simulator experimentally realize model its out-of-equilibrium properties.