A tensor network is a representation of a tensor by contracting selected indices of smaller tensors according to a graph. Each internal edge labels
a summed index, while uncontracted indices label the output tensor.
For example, the matrix product 
contracts the index 
of two tensors. The dimension
of an internal index is its bond dimension.
A projected entangled-pair state uses one tensor at each site of a lattice, with internal indices on lattice edges and one output index for the local Hilbert space. A small bond dimension limits the number of parameters but does not itself guarantee an accurate approximation to a particular ground state.
