4 problems

Let ${\mathbf a}_1,{mathbf a}_2:= (\sqrt{3}/2, \pm1/2)$ generate the triangular lattice ${\mathbb L}_2$, and let ${\mathbb L}_6$ be the triangular sublattice defining a six-atom gr…

Nonexistence conjecture. The flat bands under consideration do not have compact localized states.

Nonexistence conjecture. Unlike flat bands in short-ranged translationally invariant Hamiltonians, the considered $E=0$ flat bands do not host compact localized states.

Mapping hypothesis. Any quantum system described by the Hubbard model or a tight-binding model, both in equilibrium and non-equilibrium situations, can be mapped to a classical epi…