Functional Bethe ansatz methods for the open XXX chain

Understand

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields.

• The spectral problem for this model can be formulated in terms of functional equations obtained by separation of variables or, equivalently, from the fusion of transfer matrices.
• For generic boundary conditions the eigenvalues cannot be obtained from the solution of finitely many algebraic Bethe equations.
• Based on careful finite size studies of the analytic properties of the underlying hierarchy of transfer matrices we devise two approaches to analyze the functional equations.