  We study properties of the lowest energy states at non-zero total momentum
(yrast states) of the Hubbard model for spin-1/2 fermions in the quantum ring
configuration with attractive on-site interaction at low density. In the
one-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz,
while for the crossover into the 2D regime we use the
Full-Configuration-Interaction Quantum Monte-Carlo method (FCIQMC) to obtain
the yrast states for the spin-balanced Fermi system. We show how the yrast
excitation spectrum changes from the 1D to the 2D regime and how pairing
affects the yrast spectra. We also find signatures of fragmented condensation
for certain yrast states usually associated with dark solitons.
