Abstract
We shall present the construction of Tensor Networks using the tools of Conformal Field Theory (CFT).
The basic idea of this approach is to replace the finite dimensional tensors, used to describe the low energy states of local lattice Hamiltonians, by the primary fields of CFT. In doing so the ancilla space, that supports the entanglement, becomes infinite dimensional and is given by the representation spaces of the underlying CFT.
The construction shares strong similarities with the use of CFT in the study of the Fractional Quantum Hall wave functions. This fact allows the construction of lattice versions of the Laughlin states, the Moore-Read states, etc.
We shall give an overall account of this approach and discuss future developments.