Bound-states of particles are an interesting problem in quantum mechanics dating back to 1931 Bethe's solution of spin-1/2 Heisenberg chain. These exotic composite states are realized in quantum magnets and are detectable in inelastic neutron scattering (INS) experiments. Owing to recent advances in matrix-product-states based algorithms,
they can be numerically determined by computing Dynamical Structure Factor (DSF) of underlying spin models. We realize bound-states in three illustrative scenarios - (a) one dimensional Heisenberg ferromagnet where by studying temperature dependence of DSF we show that the bound-states appear as a well-defined excitation in temperature ranges J/12 (...) T (...)J/3, pointing to the possibility of its direct detection with INS
experiments [1], (b) spin-1/2 ladders close to magnetic-field induced phase transition where high-energy mode-splits observed in INS experiments on (C5H12N)2CuBr4 (BPCB) [2] are shown to be
bound-states of triplets by zero temperature simulations on the frustrated ladder. Upon decreasing the frustration, the well-defined bound-state modes evolves into the observed split-feature in spin ladder [3],
(c) The Shastry Sutherland compound SrCu2(BO3)2 in magnetic field, where INS experiments conducted at high-fields up to the onset of 1/8-magnetization plateau (at _ 27 T) and our zero-temperature numerical simulations on the adapted spin-model indicate a condensation of the spin-2 bound-state of triplets at 21 T, resulting in a field-induced
spin-nematic phase [4].