The tensor network representation of a state in higher dimensions, say a projected entangled-pair state (PEPS), is typically obtained indirectly through variational optimization or imaginary-time Hamiltonian evolution. Here, we propose a divide-and-conquer approach to directly construct a PEPS representation for free-fermion states admitting descriptions in terms of filling exponentially localized Wannier functions. Our approach relies on first obtaining a tree tensor network description of the state in local subregions. Next, a stacking procedure is used to combine the local trees into a PEPS. Lastly, the local tensors are compressed to obtain a more efficient description. We demonstrate our construction for states in one and two dimensions, including the ground state of an obstructed atomic insulator on the square lattice.
@article{arxiv.2308.09377,
title = {Stacked tree construction for free-fermion projected entangled pair states},
author = {Yuman He and Kangle Li and Yanbai Zhang and Hoi Chun Po},
journal= {arXiv preprint arXiv:2308.09377},
year = {2025}
}