7 problems

FOEL conjecture. Every ferromagnetic XXX model on any finite graph has the FOEL property.

Continuous-spectrum accumulation conjecture. There is no other continuous spectrum close to $-j|B|$, and therefore $-j|B|$ is purely an accumulation point of eigenvectors.

Let $\mu \in (0,4d)$ be the chemical potential, and let $U$ be the Hubbard interaction strength. Denote by $E_{\mu,U}^{(\mathrm{hf})}$ and $E_{\mu,U}^{(\mathrm{hfz})}$ the minimal…

Let $U$ be the repulsive coupling, $t$ the nearest-neighbor hopping strength, and let $u$ denote the filling, with half-filling corresponding to $u=1/2$. **Strong-coupling ferrom…

Lower-bound conjecture. The lower bound above holds for every $\mathbf{m}\in\mathcal{M}$.

Let a Hubbard model be obtained by adding a small perturbation to the hopping Hamiltonian of a flat-band model, so that its lowest single-electron band is slightly dispersive, and…

Mielke–Tasaki stability-class conjecture. Mielke–Tasaki flat-band ferromagnetism is related to a new stability class.