  We study quantum entanglements induced on product states by the action of
8-vertex braid matrices, rendered unitary with purely imaginary spectral
parameters (rapidity). The unitarity is displayed via the "canonical
factorization" of the coefficients of the projectors spanning the basis. This
adds one more new facet to the famous and fascinating features of the 8-vertex
model. The double periodicity and the analytic properties of the elliptic
functions involved lead to a rich structure of the 3-tangle quantifying the
entanglement. We thus explore the complex relationship between topological and
quantum entanglement.
