10 problems

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…

Universality conjecture. For an arbitrary Hubbard–Stratonovich factorization of this form, the quantity $DG$ is always given by the matrix displayed in equation (3.63) of the sourc…

Hirsch's conjecture. The gap $\Delta$ vanishes like

The model describes dressed bound fermion pairs with total quasi-momentum $k\in\mathbb{T}^{2}$, arising as eigenstates associated with the eigenvalue $\mathrm{E}(\mathrm{U},k)$ and…

Consider the two-dimensional square-lattice Hubbard model with chemical potential $bc$ slightly smaller than $2$. Vieri's conjecture. The ground state of this model is a non-Fermi…

Imaginary-hopping Hubbard commutant conjecture.

Center conjecture.

The Hubbard model is an extended lattice model in one, two, or three dimensions used as a paradigm for strongly correlated systems; its two-dimensional version is the 2D Hubbard mo…

A Fermi gas in two spatial dimensions is expected to exhibit behavior similar to that of a one-dimensional Luttinger liquid. Anderson's conjecture. A two-dimensional Fermi gas shou…