The lambda model is a one parameter deformation of the principal chiral model
that arises when regularizing the non-compactness of a non-abelian T dual in
string theory. It is a current-current deformation of a WZW model that is known
to be integrable at the classical and quantum level. The standard techniques of
the quantum inverse scattering method cannot be applied because the Poisson
bracket is non ultra-local. Inspired by an approach of Faddeev and Reshetikhin,
we show that in this class of models, there is a way to deform the symplectic
structure of the theory leading to a much simpler theory that is ultra-local
and can be quantized on the lattice whilst preserving integrability. This
lattice theory takes the form of a generalized spin chain that can be solved by
standard algebraic Bethe Ansatz techniques. We then argue that the IR limit of
the lattice theory lies in the universality class of the lambda model implying
that the spin chain provides a way to apply the quantum inverse scattering
method to this non ultra-local theory. This points to a way of applying the
same ideas to other lambda models and potentially the string world-sheet theory
in the gauge-gravity correspondence.Comment: 49 Page
