An exact solution to asymptotic Bethe equation

We present an exact solution to the asymptotic Bethe equation of weakly anisotropic Heisenberg spin chain, which is a set of non-linear algebraic equations. The solution describes the low-energy excitations above ferromagnetic ground state with fixed magnetisation, and it has a close relation to generalised Jacobi polynomial. It is equivalent to a generalised Stieltjes problem and in the continuous limit, it becomes a Riemann-Hilbert problem closely related to the finite-gap solutions of classical Landau-Lifshitz field theory.

Automated summary

The study presents an exact solution to the asymptotic Bethe equation of weakly anisotropic Heisenberg spin chain, describing low-energy excitations above the ferromagnetic ground state with a fixed magnetization and closely related to generalised Jacobi polynomial. It is equivalent to a generalised Stieltjes problem and in the continuous limit, becomes a Riemann-Hilbert problem closely related to the finite-gap solutions of the classical Landau-Lifshitz field theory.