How local is the information in MPS/PEPS tensor networks?

Understand

Two dimensional tensor networks such as projected entangled pairs states (PEPS) are generally hard to contract.

• This is arguably the main reason why variational tensor network methods in 2D are still not as successful as in 1D.
• However, this is not necessarily the case if the tensor network represents a gapped ground state of a local Hamiltonian; such states are subject to many constraints and contain much more structure.
• In this paper we introduce a new approach for approximating the expectation value of a local observable in ground states of local Hamiltonians that are represented as PEPS tensor-networks.