10 problems

Open-chain product conjecture. Numerical evaluation leads to the conjecture that

Consider the periodic XXZ spin chain at anisotropy $\Delta=-\frac12$ with odd length $L=2n+1$, and let $\psi(1,2,\ldots,n)$ and $\psi(1,3,\ldots,2n-1)$ be respectively the smallest…

Let $\langle\sigma_m^z\sigma_1^z\rangle$ denote the zero-temperature two-point correlation function of the $XXZ$ spin chain at separation $m$. In the critical regime, the distance…

Let $r$ be odd, and distinguish cases (i)–(iv) according to the parity of $\frac{{\tt s}+S^z}{r}-S^z$ and the sign of ${\tt k}$, with $\tilde{\tt m}$ and $\tilde{\tt s}$ defined by…

Let $T>0$ be fixed, let $m$ denote the spatial separation, and let $t$ denote time. For the transverse thermal dynamical two-point function of the XXZ spin-$1/2$ chain, let…

Let $\mathfrak{q}=e^{i\pi/p}$ with $p\in\mathbb{N}\backslash\{0,1\}$, and let $\alpha_l,\alpha_r\in\mathbb{C}\backslash\mathbb{Z}$ satisfy $\alpha_l+\alpha_r\notin\mathbb{Z}$. Writ…

Let $\mathfrak{q}\in\mathbb{C}\backslash\mathfrak{q}^{i\pi\mathbb{Q}}$, let $\mathfrak{q}^{\alpha_l},\mathfrak{q}^{\alpha_r}\in\mathbb{C}\backslash\{\pm\mathfrak{q}^{\mathbb{Z}}\}$…

Let $Z(\mathrm{i}t)$ be the return amplitude of the XXZ spin chain with domain wall initial state, let $\gamma$ be the interaction parameter, and let $p,q$ be integers specifying w…

Let $q$ and $r$ satisfy $-1<q<0$ and $-1\leq r\leq 1$, let $s\in{\bf R}$, and let $V={\bf C}^2$ have natural basis $\{v_+,v_-\}$. For $i=0,1$, define the half-infinite spin-chain s…

Let $E^{e}_{2n}(k)$ denote the emptiness formation probability (EFP) of a string of $k$ consecutive up spins in the XXZ spin chain with $2n$ sites and twisted-periodic boundary con…