Abstract

Rational Q-system is an efficient method for solving Bethe ansatz equations (BAE). One important feature of this method is that, unlike solving BAE directly, it gives only physical solutions of BAE. Therefore, it is intimately related to the completeness problem of Bethe ansatz. In this talk, I will first introduce the rational Q-system and discuss the completeness problem of the spin-$1/2$ Heisenberg spin chain. Then I will move to the discussion of the spin-$s$ Heisenberg spin chain where the situation is more complicated. The key new feature here is that repeated roots are allowed. I will present the rational Q-system for the higher spin models and discuss the completeness problem for the spin-$s$ Heisenberg spin chain. The solution of the proposed Q-system gives precisely the all the physical solutions required by completeness of Bethe ansatz.