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Here the line shape of the up- and down-spin one-particle spectral functionsat and in the (k,energy)-plane's vicinity of their cusp singularities isstudied for the Mott-Hubbard insulator described by the 1D Hubbard model withone fermion per site at zero and finite magnetic fields. At zero field they canbe accessed in terms of electrons by photoemission experiments. At finitefield, such functions and corresponding interplay of correlations andmagnetic-field effects refer to an involved non-perturbative many-particleproblem that is poorly understood. The Mott-Hubbard gap that separates theaddition and removal spectral functions is calculated for all spin densitiesand interaction values. The qualitative differences in the one-particleproperties of the Mott-Hubbard insulator and corresponding doped insulator arealso investigated. The relation of our theoretical results and predictions toboth condensed-matter and ultracold spin-1/2 atom systems is discussed.

One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields