Key points are not available for this paper at this time.
We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows us to extend the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension. We illustrate our procedure with the Lieb-Liniger model.
Verstraete et al. (Fri,) studied this question.