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

The spectra and role in the spin dynamical properties of bound states of elementary magnetic excitations named Bethe strings that occur in some integrable spin and electronic one-dimensional models have recently been identified and realized in several materials by experiments. Corresponding theoretical studies have usually relied on the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field. At the isotropic point, it describes the large onsite repulsion U limit of the spin degrees of freedom of the one-dimensional fermionic Hubbard model with one electron per site in a magnetic field h. In this paper we consider the thermodynamic limit and study the effects of lowering the latter quantum problem ratio u = U/4t, where t is the first-neighbor transfer integral, on the line-shape singularities in (k, omega)-plane regions at and just above the lower thresholds of the transverse and longitudinal spin dynamical structure factors. The most significant spectral weight contribution from Bethe strings leads to a gapped continuum in the spectrum of the spin dynamical structure factor S-+(-) (k, omega). Our study focuses on the line shape singularities at and just above the gapped lower threshold of that continuum, which have been identified in experiments. Our results are consistent with the contribution of Bethe strings to S-zz(k, omega) being small at low spin densities and becoming negligible upon increasing that density. Our results provide physically important information about how electron itinerancy affects the spin dynamics.