Jordan blocks and the Bethe Ansatz

The Bethe Ansatz, both in its coordinate and its algebraic form, allows us to systematically construct the eigenvalues and eigenvectors of quantum integrable systems. However, recently new quantum integrable models have been constructed where these methods are not able to construct the full Hilbert space. The common characteristic of these models is that they have non-diagonalisable Hamiltonians. In this talk, I'll show why the Bethe Ansatz doesn't work on these models and propose ways around this problem.