Generalised ansatz for continuous Matrix Product States

Abstract: Recently it was shown that continuous Matrix Product States (cMPS) cannot express the continuum limit state of any Matrix Product State (MPS), according to a certain natural definition of the latter. The missing element is a projector in the transfer matrix of the MPS. Here we provide a generalised ansatz of cMPS that is capable of expressing the continuum limit of any MPS. It consists of a sum of cMPS with different boundary conditions, each attached to an ancilla state. This new ansatz can be interpreted as the concatenation of a state which is at the closure of the set of cMPS together with a standard cMPS. The former can be seen as a cMPS in the thermodynamic limit, or with matrices of unbounded norm. We provide several examples and discuss the result.