Efficient representation of long-range interactions in tensor network algorithms
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.
Keywords
Cite
@article{arxiv.1807.08378,
title = {Efficient representation of long-range interactions in tensor network algorithms},
author = {Matthew J. O'Rourke and Zhendong Li and Garnet Kin-Lic Chan},
journal= {arXiv preprint arXiv:1807.08378},
year = {2018}
}
Comments
Main Document: 9 pages, 7 figures. Moved supplementary material into main text. Added more discussion of computational cost. Fixed minor errors in Figs 2c and 3a