Fast analytic solver of rational Bethe equations

Source abstract

Abstract In this note we propose an approach for a fast analytic determination of all possible sets of Bethe roots corresponding to eigenstates of rational G L ( N | M ) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional solutions, if any, are automatically correctly accounted. The key intuition behind the approach is that the equations on the Q-functions are determined solely by the Young diagram, and not by the choice of the rank of the G L symmetry. Hence we can choose arbitrary N and M that accommodate the desired representation. Then we consider all distinguished Q-functions at once, not only those following a certain Kac–Dynkin path.