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arXiv · 2308.09377

Stacked tree construction for free-fermion projected entangled pair states

Yuman He·Kangle Li·Yanbai Zhang·Hoi Chun Po
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Abstract

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.

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Yuman He, Kangle Li, Yanbai Zhang, Hoi Chun Po. 2023-08-18. Stacked tree construction for free-fermion projected entangled pair states. https://doi.org/10.1103/physrevresearch.6.l022016

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