11 problems

Zero-location conjecture. For $n<p_0$, $T^{(3)}_{n-1}(u,v)$ has two real zeros $\pm\zeta^{(3)}_{n-1}$ for some $\zeta^{(3)}_{n-1}\in\mathbf R_{>0}$, while for $n=p_0$ it has a doub…

Zero-location conjecture. All the zeros of $T^{(1)}_{n-1}(u,v)$ are located on the almost straight lines

Large-spin Bose-gas conjecture. There is a function $\gamma_\infty:(1,\infty)\times\mathbb{R}\to\mathbb{R}$ such that

For the even-site ground state $|\Psi^{(2n)}\rangle$, define … and set $\alpha_i=(1+\sigma_i^z)/2$. Korepin–Izergin–Baxter ferromagnetic-string formula. The probabilities of format…

For the even-site ground state $|\Psi^{(2n)}\rangle$, define the normalized expectation of an operator $O$ by … and define $\alpha_i=(1+\sigma_i^z)/2$. The twisted XXZ next-nearest…

Let $|\Psi^{(2n)}\rangle$ be the normalized ground-state vector of the twisted XXZ chain with $2n$ sites, let … and let $A_n$ be the number of alternating-sign $n\times n$ matrices…

Let $|\Psi^{(2n)}\rangle$ be the normalized ground-state vector of the twisted XXZ chain with $2n$ sites, and let $A_n$ denote the number of alternating-sign $n\times n$ matrices.…

Let $H^{(N)}$ be the XXZ Hamiltonian with twisted boundary conditions, with $N$ an even number of sites, twisting angle $\phi$, anisotropy $\Delta$, and total spin $z$-axis project…

Bethe-vector basis conjecture. For every $|\mathbf{x}\rangle\in\mathbb{V}$,

Completeness conjecture. The Bethe Ansatz completely determines the spectrum for all but finitely many values of $\Delta$ with $|\Delta|<\varepsilon$.

Finite-size component conjecture. For each $n\geqslant 1$,