13 problems

Let a Hubbard model have a localized domain wall structure, and consider the band-bending perturbation $H_{\rm hop} '$. The variational analysis compares the energy shifts of domai…

Wall-fusion associativity conjecture. Fusion through $\CC$ satisfies

Condensable-algebra fusion conjecture. Their relative tensor product satisfies

Separable-algebra decomposition conjecture. There is a separable algebra $B'\in\CM$ such that

Domain-wall decomposition conjecture. Any gapped domain wall of the form

Generalized pull-open conjecture. Any stable gapped domain wall ${}_B\CM_B$ is equivalent to

Let $(\mathcal{B},c)$ be a topological order, let $\mathcal{S}^{Int}_{\mathcal{B}}$ be the space of Hamiltonians realizing the intrinsic topological order $(\mathcal{B},c)$ up to i…

Let $(\mathcal{B},c)$ be a topological order, let $\mathcal{S}^c_{\mathcal{B}}$ be the space of gapped Hamiltonians realizing it, and let…

Let $F$ map invertible states and domain walls in $(d-1)$ dimensions to paths of $d$-dimensional Hamiltonians, and let $G$ map paths of $d$-dimensional Hamiltonians to invertible s…

Let $h$ denote the applied field, and let magnetisations be configurations governed by the Landau–Lifshitz–Gilbert equation in a nanowire with Dzyaloshinskii–Moriya interaction. A…

A chiral skyrmion is a localized magnetic configuration, and a chiral kink is a kink on its outer domain wall. Consider configurations with chiral kinks on an outer domain wall and…

In the Levin–Wen model based on $\operatorname{Vec}(S_3)$, let $t$ be a twist and let $A$, $G$, and $H$ denote the anyon types appearing in the twist fusion rules. Barkeshli et al.…

Uniqueness conjecture. The minimizer $U(x)$ of the energy $E$ in $X$ is unique, up to translation and gauge invariance.