  We define a class of tensor network states for spin systems where the
individual tensors are functionals of fields. The construction is based on the
path integral representation of correlators of operators in quantum field
theory. These tensor network states are infinite dimensional versions of matrix
product states and projected entangled pair states. We find the field-tensor
that generates the Haldane-Shastry wave function and extend it to two
dimensions. We give evidence that the latter underlies the topological chiral
state described by the Kalmeyer-Laughlin wave function.
