I will present a study of continuum limits of Matrix Product States (MPS). We show that an MPS has a continuum limit if and only if its transfer matrix is an infinitely divisible channel. To prove this result, we first need to define the irreducible form of an MPS, which is a generalization of the canonical form. This result also implies that the continuum limit of an MPS can generally not be described by a continuous MPS -- I will mention a possible generalization of the latter class.

Joint work with M. Balanzo-Juando, I. Cirac, D. Perez-Garcia and N. Schuch.
Based on arXiv:1708.00880 and arxiv:1708.00029.