17 problems

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 $N=2n+1$ be odd, and let $a_1,\ldots,a_k$ denote the local observables defining the ferromagnetic-string correlations. Ferromagnetic-string probability conjecture. The correlat…

Let $N=2n+1$ be odd, and let $a_j$ denote the local observable used for the spin-chain correlations. Correlation formula conjecture. The next-nearest-neighbor correlation is … The…

Let $N=2n+1$ be odd, let ${\mathcal N}_n$ be the norm of the ground state, and let the state vector have components in the spin-configuration basis. Sum-of-components conjecture. T…

Let $n$ be the rank parameter of the type $B$ MultiTASEP, and write $\langle a,b\rangle$ for the two-point correlation of entries in the last two positions, with barred symbols den…

Consider the massless time-like regime of the XX chain and the complex correlation function $(-1)^m\langle\sigma^-_1(0)\sigma^+_{m+1}(t)\rangle$. Positivity conjecture. Both its re…

Let $r(m,t,h):=(-1)^m\langle \sigma^-_{1}(0)\sigma^+_{m+1}(t)\rangle_{-h,T}/I_m(t)$ be the ratio formed from the time-like correlation function and its leading asymptotic factor. F…

Witte–Forrester conjecture. For even $l\leq 2$,

Let $w=(w_a)$ denote the cyclic multispecies TASEP word, and let $E_{i_1,\dots,i_r}$ and $E_{j_{r+1},\dots,j_{r+s}}$ denote the corresponding nearest-neighbour block probabilities.…

Let $w=(w_a)$ denote the cyclic multispecies TASEP word, and let $E_{i_1,\dots,i_r}$ denote the joint probability of seeing $i_a$ in position $a$, for $a=1,\dots,r$. One-apart inde…

Let $E_{i_1,\dots,i_r}$ denote the joint probability of seeing particle types $i_a$ in positions $a$, for $a=1,\dots,r$. Far-particle factorization conjecture. For any…

Let $E_{i_1,\dots,i_r}$ denote the joint probability of seeing particle types $i_a$ in positions $a$, for $a=1,\dots,r$. Increasing-correlation conjecture. If … then … This extends…

Let $\rho_N(x,t)$ be the finite-volume reduced density matrix. Set ${\mathcal B}_L=\{n\in\mathbb Z:-w_L<n<w_L\}$,…

Let $q_j,r_j,s_j=7$, ${\bf x}_j\in{\mathbb R}^2$, and $t_j\in{\mathbb C}$ for $j=1,2,\ldots,N$, with $N\in{\mathbb N}$. Let … be the renormalized fermion operators, where $K$ is th…

Let $\psi^{\sharp}$ denote either spin field, let $\lambdaup>0$ be sufficiently small, and let $\Lambdaup\subset\mathbb{Z}^d$ be a finite volume. For even $n\geq 2$, write…

Let $N=1,2,\dots$, let $\varkappa_j=(\nu_j,\eta_j,\tau_j)\in\mathcal D$ be distinct triples, and let $\Omega_j=\Omega(\nu_j,\eta_j,\tau_j)$. The correlation formula of Theorem 1.17…