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The spectra and role in the spin dynamical properties of bound states ofelementary magnetic excitations named Bethe strings that occur in someintegrable spin and electronic one-dimensional models have recently beenidentified and realized in several materials by experiments. Correspondingtheoretical studies have usually relied on the one-dimensional spin-1/2Heisenberg antiferromagnet in a magnetic field. At the isotropic point, itdescribes the large onsite repulsion U limit of the spin degrees of freedom ofthe one-dimensional fermionic Hubbard model with one electron per site in amagnetic field h. In this paper we consider the thermodynamic limit and studythe effects of lowering the latter quantum problem ratio u=U/4t, where t is thefirst-neighbor transfer integral, on the line-shape singularities in regions atand just above the lower thresholds of the transverse and longitudinal spindynamical structure factors. The most significant spectral weight contributionfrom Bethe strings leads to a gapped continuum in the spectrum of the spindynamical structure factor +-. Our study focuses on the line shapesingularities at and just above the gapped lower threshold of that continuum,which have been identified in experiments. Our results are consistent with thecontribution of Bethe strings to the spin dynamical structure factor zz beingsmall at low spin densities and becoming negligible upon increasing thatdensity. Our results provide physically important information about howelectron itinerancy affects the spin dynamics.

Bethe strings in the spin dynamical structure factor of the Mott-Hubbard phase in one-dimensional fermionic Hubbard model