Algebraic Structure of Finite-Size Bethe Solutions in the Heisenberg Chain
The paper investigates whether exact solutions to quantum models, like the Heisenberg chain, are always easy to write down analytically. It found that while the equations defining solutions (Bethe roots) are always present, they become mathematically unsolvable in radicals for chains of eight sites or more. However, the ground state energy and coefficients remain solvable up to eight sites. This shows a crucial distinction between formal mathematical solvability and practical analytic tractability.