Consistent refinement of Bethe strings for spin and electron models and a new non-Bethe solution

Well known Bethe strings, such as those in spin chains, the δ-electron gas, and the Hubbard and t-J models, are shown to be imprecise, while their consistent refinement along with a new non-Bethe r-string is discovered. A connection with earlier results is established and the string hypothesis problem is discussed in the light of the present findings. (author). Letter-to-the-editor