Efficient representation of long-range interactions in tensor network algorithms

TL;DR

This paper presents a practical method to efficiently encode long-range interactions in two-dimensional tensor network algorithms using PEPOs, enabling more effective simulations of physical systems with such interactions.

Contribution

The authors introduce a novel PEPO construction that represents long-range interactions as a sum of small-bond-dimension ancillary PEPOs, improving simulation efficiency.

Findings

Efficient representation of long-range interactions in 2D tensor networks.

Construction of PEPOs as sums of small ancillary PEPOs.

Facilitates numerical simulations with long-range interactions.

Abstract

We describe a practical and efficient approach to represent physically realistic long-range interactions in two-dimensional tensor network algorithms via projected entangled-pair operators (PEPOs). We express the long-range interaction as a linear combination of correlation functions of an auxiliary system with only nearest-neighbor interactions. To obtain a smooth and radially isotropic interaction across all length scales, we map the physical lattice to an auxiliary lattice of expanded size. Our construction yields a long-range PEPO as a sum of ancillary PEPOs, each of small, constant bond dimension. This representation enables efficient numerical simulations with long-range interactions using projected entangled pair states.