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In this paper the spin configurations of the ground state and one- andtwo-electron excited states of the Hubbard model on the square lattice arestudied. We profit from a general rotated-electron description, which isconsistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. Forrotated electrons, doubly and single occupancy are good quantum numbers foron-site repulsion $U>0$. The above states are within that description generatedby occupancy configurations of charge $c$ fermions and spin-singlet two-spinon$s1$ bond particles. Those describe the charge and spin degrees of freedom,respectively, of the rotated electrons that singly occupy sites. While the $c$fermions have no internal structure, that of the spin-neutral $s1$bond-particle occupancy configurations is here described in terms of spinonoccupancies of a well-defined effective spin lattice. In reference\cite{companion} it is confirmed that our results contribute to the furtherunderstanding of the role of electronic correlations in the spin spectrum ofthe parent compound La$_2$CuO$_4$. They are also of interest for studies ofultra-cold fermionic atoms on an optical lattice.

Ground-state two-spinon bonds in the Hubbard model on a square lattice