Can electron interactions alone produce altermagnetism?
In plain words
Known altermagnets get their spin splitting from the arrangement of atoms in the crystal. Theory suggests that repulsion between electrons could create the same kind of spin-split state spontaneously, but no unbiased calculation has shown it in a simple model.
Precise statement
Find a lattice model of interacting electrons (for example an extended Hubbard model with on-site U and nearest-neighbor V) whose paramagnetic phase has no symmetry-inequivalent magnetic sublattices and whose ground state spontaneously develops a d-wave or g-wave spin-split Fermi surface with zero net magnetization, established by unbiased numerics (DMRG, auxiliary-field quantum Monte Carlo or tensor networks) beyond mean-field theory. An answer is the model, the parameter range and the order parameter.
What would settle it
An unbiased ground-state calculation with finite-size extrapolation of the spin-split order parameter in the proposed model.