Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917006351007744 |
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| author | Xu, Xia-Ze Lin, Tong-Yu Zhang, Guang-Ming |
| author_facet | Xu, Xia-Ze Lin, Tong-Yu Zhang, Guang-Ming |
| contents | Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational cost associated with evaluating the free energy density and its gradient. This process requires contracting a triple-layer tensor network composed of a projected entangled pair operator and projected entangled pair states. In this paper, we employ a split corner-transfer renormalization group scheme tailored for the contraction of such a triple-layer network, which reduces the computational complexity while keeping high accuracy. Through numerical benchmarks on the three-dimensional classical Ising model, we demonstrate that the proposed scheme achieves numerical results comparable to the most recent Monte Carlo simulations, providing a substantial speedup over previous variational tensor network approaches. This makes this method well-suited for efficient gradient-based optimization in three-dimensional tensor network simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient optimization of variational tensor-network approach to three-dimensional statistical systems Xu, Xia-Ze Lin, Tong-Yu Zhang, Guang-Ming Statistical Mechanics Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational cost associated with evaluating the free energy density and its gradient. This process requires contracting a triple-layer tensor network composed of a projected entangled pair operator and projected entangled pair states. In this paper, we employ a split corner-transfer renormalization group scheme tailored for the contraction of such a triple-layer network, which reduces the computational complexity while keeping high accuracy. Through numerical benchmarks on the three-dimensional classical Ising model, we demonstrate that the proposed scheme achieves numerical results comparable to the most recent Monte Carlo simulations, providing a substantial speedup over previous variational tensor network approaches. This makes this method well-suited for efficient gradient-based optimization in three-dimensional tensor network simulations. |
| title | Efficient optimization of variational tensor-network approach to three-dimensional statistical systems |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2506.19339 |