Efficient Two Dimensional Tensor Network Algorithms for Systems with Long-Range Interactions

Current state-of-the-art tensor network algorithms in two dimensions, the most predominant being infinite projected entangled-pair states (iPEPS), have not yet advanced beyond the study of local lattice models. In order to utilize the power of these methods to study systems with physically realistic long-range interactions, we discuss a practical and efficient representation of the Hamiltonian of such systems as a projected entangled-pair operator (PEPO). We express the long-range interaction as a linear combination of correlation functions of an auxiliary system with only nearest neighbor interactions. This construction yields a long-range PEPO as a sum of ancillary PEPOs, each of small, constant bond dimension. Applications of this PEPO formulation to iPEPS simulations of model systems will be discussed.