Field tensor network states

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.