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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.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"An unbiased ground-state calculation with finite-size extrapolation of the spin-split order parameter in the proposed model.","status_note":"","title":"Can electron interactions alone produce 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