19 problems

Let $J_2(p)$ denote the variational problem considered in the source, with exponent $p$. The authors of the cited work conjecture that the nonexistence conjecture for $J_2(p)$.…

For $m$ fermionic modes, let $\mathcal H_m$ be the corresponding Hilbert space, let $\mathcal G_m^\pm$ denote the pure fermionic Gaussian states, and let … be the projector definin…

Evenness conjecture. The evenness of \vp^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta} can be derived from either the LTS condition alone or the Gibbs c…

Prosen's conjecture. The total number of proper eigenstates of $\hat{\mathcal{M}}_{\ell,m}$ is equal to the dimension of $\mathcal{V}_{\ell,m}^r$.

Center conjecture. The center is

Let ${\rm GICAR}$ denote the groupoid $C^*$-algebra framework for fermionic observables, and let ${\mathcal G}_N$ be the groupoids associated with the $N$-particle sectors. Their m…

Let interacting spin-$\tfrac{1}{2}$ fermions have a spatial wave function, and consider its nodal set separating regions where the wave function has different signs. Nodal-domain c…

Let point-group or space-group symmetry act on an interacting fermionic system, and impose the crystalline principle and the relevant spin-statistics relations. Crystalline extensi…

Let $G_f=\mathbb{Z}_2^f\times_{\omega_2}G_b$ be a fermionic symmetry group, with fermion parity subgroup $\mathbb{Z}_2^f$, and consider FSPT constructions subject to obstruction an…

Let $\mathcal{H}_N$ be the Hilbert space of $N$ fermionic particles, let $\Psi_N\in\mathcal{H}_N$ be normalized, and set $\rho_N=|\Psi_N\rangle\langle\Psi_N|$. Denote by $\gamma_2$…

Fermi-surface topology conjecture. The entanglement properties of critical fermion models are entirely determined by the topology of their Fermi surface; in the setting considered,…

Fermi-surface topology conjecture. The critical behavior of fermionic lattice models is completely determined by the topology of their Fermi surface.

For each $N$, let the many-fermion dynamics with Coulomb interaction and its effective Hartree dynamics be compared in the setting of the paper, where the convergence estimate has…

Let $G^f$ be a fermionic symmetry group and let $\cE=\operatorname{sRep}(G^f)$ be the corresponding symmetric fusion category. Let $\cM$ be a modular extension of $\cE$, and let…

Let $\varrho$ be a pure fermionic density operator, let $\varrho_p$ denote its conventional $p$-particle reduced density matrix, and let … be the particle-reduction operation, with…

Let $|\Psi_N\rangle$ be an $N$-fermion state with natural orbitals (NOs) $\{|i\rangle\}_{i=1}^d$ and natural occupation numbers (NONs) $\vec{\lambda}$ having one degeneracy,…

Let $M$ be odd, and let $\mathcal{S}$ denote the single-occupancy subspace of the $N$-fermion Hilbert space. Let $\mathcal{U}_M$ be the candidate subspace described in Proposition…

Topological phases of fermionic systems are organized by symmetry constraints on gapped quadratic fermion Hamiltonians; the relevant symmetries include unitary and antiunitary oper…

Generic optimality conjecture. The protocol given by the operators $\hat{D}$ and $\hat{V}$ is generically a good, if not the best, choice within the introduced family of distillati…