Single-layer framework of variational tensor network states
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918450272665600 |
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| author | Chen, Hongyu Fu, Yangfeng Yu, Weiqiang Yu, Rong Xie, Z. Y. |
| author_facet | Chen, Hongyu Fu, Yangfeng Yu, Weiqiang Yu, Rong Xie, Z. Y. |
| contents | We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the automatic differentiation technique, our approach can reduce the computational cost by three orders of magnitude in bond dimension, and therefore enables highly efficient variational ground-state calculations. We demonstrate the capability of this framework through two quantum spin models: the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Even without GPU acceleration or symmetry implementation, we have achieved a bond dimension of nine and obtained accurate ground-state energy and consistent order parameters compared to prior studies. In particular, we confirm the existence of an intermediate empty-plaquette valence bond solid ground state in the Shastry-Sutherland model. We have further discussed the convergence of the algorithm and its potential improvements. Our work provides a promising route for large-scale tensor network calculations of two-dimensional quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Single-layer framework of variational tensor network states Chen, Hongyu Fu, Yangfeng Yu, Weiqiang Yu, Rong Xie, Z. Y. Strongly Correlated Electrons We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the automatic differentiation technique, our approach can reduce the computational cost by three orders of magnitude in bond dimension, and therefore enables highly efficient variational ground-state calculations. We demonstrate the capability of this framework through two quantum spin models: the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Even without GPU acceleration or symmetry implementation, we have achieved a bond dimension of nine and obtained accurate ground-state energy and consistent order parameters compared to prior studies. In particular, we confirm the existence of an intermediate empty-plaquette valence bond solid ground state in the Shastry-Sutherland model. We have further discussed the convergence of the algorithm and its potential improvements. Our work provides a promising route for large-scale tensor network calculations of two-dimensional quantum systems. |
| title | Single-layer framework of variational tensor network states |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2512.14414 |