Stacked tree construction for free-fermion projected entangled pair states

• URL: http://arxiv.org/abs/2308.09377v1
• Date: Fri, 18 Aug 2023 08:13:35 GMT
• Title: Stacked tree construction for free-fermion projected entangled pair states
• Authors: Yuman He, Kangle Li, Yanbai Zhang, Hoi Chun Po
• Abstract summary: We propose a divide-and-conquer approach to construct a PEPS representation for free-fermion states admitting descriptions in terms of filling exponentially localized Wannier functions. We demonstrate our construction for states in one and two dimensions, including the ground state of an obstructed atomic insulator on the square lattice.
• Score: 0.6144680854063939
• License: http://creativecommons.org/licenses/by/4.0/
• 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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