5 problems

Let $p(\gamma)$ be the dimensionless pressure of the Lieb-Liniger Bose gas, and let $\mathcal P_n(\gamma)$ be polynomials in $\gamma$. The partial resummation conjecture. The stron…

Consider the repulsive Lieb-Liniger model, whose low-energy effective hydrodynamic description is given by the quantum Korteweg–de Vries equation. Its excitations include Lieb's ty…

Let $\mathcal{L}_n(\gamma)$ be the degree-$n-1$ polynomial appearing in the conjectured decomposition of the $n$th-complexity contribution to the dimensionless Lieb–Liniger ground-…

Let $e(\gamma)=\sum_{n=0}^{+\infty}e_n(\gamma)$ be the dimensionless ground-state energy, decomposed into terms of complexity $n$, and let $e^{TG}=\pi^2/3$ denote its value in the…

Overlap formula conjecture. The overlap of the unnormalised initial wave function with a generic paired Bethe state is