Bethe roots in the finite Heisenberg chain ground state become Galois unsolvable for 8 or more sites, while wavefunction coefficients do so for 10 or more sites.
Faddeev, Algebraic aspects of the Bethe ansatz, Inter- national Journal of Modern Physics A10, 1845 (1995)
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Galois Solvability of Finite-Size Bethe Solutions in the Heisenberg Chain
Bethe roots in the finite Heisenberg chain ground state become Galois unsolvable for 8 or more sites, while wavefunction coefficients do so for 10 or more sites.