Single-layer tensor network approach for three-dimensional quantum systems

• URL: http://arxiv.org/abs/2405.01489v2
• Date: Tue, 20 Aug 2024 14:42:39 GMT
• Title: Single-layer tensor network approach for three-dimensional quantum systems
• Authors: Illia Lukin, Andrii Sotnikov,
• Abstract summary: We utilize the multi-layer structure of these tensor networks to simplify the contraction. We benchmark our results on the cubic lattice Heisenberg model, reaching the bond dimension D = 7.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to largely simplify the contraction. The proposed approach involves the usage of the layer structure both to simplify the search for the boundary projected entangled pair states and the single-layer mapping of the final corner transfer matrix renormalization group contraction. We benchmark our results on the cubic lattice Heisenberg model, reaching the bond dimension D = 7, and find a good agreement with the previous results.

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