4 problems

The W-state signature conjecture. If such a translation-invariant Hamiltonian is tuned so that the zero-mode $|W_1\rangle$-like state and the product state…

Boundary Gibbs-state conjecture. The parent Hamiltonian of the PEPS is gapped if and only if the boundary states can be written as Gibbs states of one-dimensional short-range Hamil…

Emergence of the renormalized Gibbs measure. In the limit $\lambda=T^{-1}\to0$, one obtains the renormalized Gibbs measure in the sense that

Area bound conjecture. There exists such a function $f$ for every gapped one-dimensional model, so the entanglement entropy is bounded in terms of the ratio of the Lieb–Robinson ve…