10 problems

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

Let $J$ be a $7 \times 7$ Jacobi matrix with symmetric spectrum that realizes perfect state transfer (PST). Its early state exclusion (ESE) property means that no state is excluded…

Let $\mathfrak{g}$ be the Lie algebra generated by the raising and lowering operators of the periodic Fredkin chain with $N$ sites. Let $\mathrm{S}^z$ be the third component of the…

Let $\mathfrak{g}$ be the Lie algebra generated by the raising and lowering operators $\Sigma^\pm$ of the periodic Fredkin chain with $N$ sites, and set $n=\lceil N/2\rceil$. B- an…

Anti-adjoint representation conjecture. There exist coefficients $\gamma_k$ such that

Let $\Sigma^\pm$ be the raising and lowering operators for the periodic Fredkin chain, let $C$ be the cyclic shift operator, and let $\mathrm{H}$ be its Hamiltonian. An eigenstate…

Raising and lowering operator conjecture. There exist raising and lowering operators $\Sigma^\pm$ satisfying

Component-sum conjecture. We have

Let $1\leqslant m\leqslant N$ and let $N_1,\dots,N_m\geqslant 1$ be integers satisfying $N=N_1+\dots+N_m$. For the ground-state vectors of the open XXZ chain, define … The scalar p…

Logarithmic entanglement-scaling conjecture. The entanglement entropy of any such block, to leading order, scales as