  In this paper we construct the continuous Matrix Product State (MPS)
representation of the vacuum of the field theory corresponding to the
continuous limit of an Ising model. We do this by exploiting the observation
made by Hastings and Mahajan in [Phys. Rev. A \textbf{91}, 032306 (2015)] that
the Euclidean time evolution generates a continuous MPS along the time
direction. We exploit this fact, together with the emerging Lorentz invariance
at the critical point in order to identify the matrix product representation of
the quantum field theory (QFT) vacuum with the continuous MPS in the time
direction (tMPS). We explicitly construct the tMPS and check these statements
by comparing the physical properties of the tMPS with those of the standard
ground MPS. We furthermore identify the QFT that the tMPS encodes with the
field theory emerging from taking the continuous limit of a weakly perturbed
Ising model by a parallel field first analyzed by Zamolodchikov.
