8 problems

Let the spin $1/2$ XXZ Heisenberg model on a three-dimensional lattice be defined by … with $\Delta>1$. A 111 interface Gibbs-state conjecture asserts that the model has a Gibbs st…

Perfectness conjecture. Every perfect finite-order planon-only theory of excitations can be realized by a suitable quantum lattice model.

Perfectness conjecture. Every perfect theory of excitations can be realized by a quantum lattice model with a spatially local Hamiltonian.

Let $Z_N$ denote the cyclic symmetry acting on the model, and let $\mathbf{F}^{(l)}$ be the deformed bulk theory obtained by inserting a $Z_N$ twisted boundary condition, with defo…

R-matrix conjecture. An intertwining R matrix $\mathsf{R}^{\rm FM}_{(a,b)(c,d)}(z,w,\theta)$ exists and satisfies

Integrability conjecture. The Hamiltonian $\mathsf{H}^{\rm FM}(r,\theta)$ is integrable for arbitrary $r\in\mathbb{Z}_{>0}$ and $0\leq\theta<2\pi$. This proposes an integrable inte…

Let the spin-$1/2$ XXZ model and the spin-1 ZF model be evaluated at root-of-unity values of the anisotropy. A Hamiltonian is $U(1)$-invariant when it commutes with both Onsager ge…

Conjecture on further LRB implications. The LRB encloses further theoretical implications, such as the clustering of correlations or the efficiency of time-dependent density matrix…