  In the context of a quantum critical spin chain whose low energy physics
corresponds to a conformal field theory (CFT), it was recently demonstrated [A.
Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks
used for numerically describing the ground state of the spin chain can also be
used to implement (discrete, approximate versions of) conformal transformations
on the lattice. In the continuum, the same conformal transformations can be
implemented through a CFT path integral on some curved spacetime. Based on this
observation, in this paper we propose to interpret the tensor networks
themselves as a path integrals on curved spacetime. This perspective assigns (a
discrete, approximate version of) a geometry to the tensor network, namely that
of the underlying curved spacetime.
