Projected Entangled-Pair State

A projected entangled-pair state (PEPS) is a tensor-network vector obtained from entangled pairs on graph edges by applying a linear map at each vertex. On an edge , choose a virtual dimension and the vector . At a vertex , apply a map from the tensor product of its incident virtual spaces to its physical Hilbert space . Contracting every virtual edge gives the physical vector. The maximum bond dimension is . The local maps need not be isometries, and the resulting vector need not be normalized.