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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14425 |
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| _version_ | 1866912967211089920 |
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| author | Fan, Chaohui Zhan, Bo Gu, Yuntian Liu, Tong Wu, Yantao Qin, Mingpu Lv, Dingshun Xiang, Tao |
| author_facet | Fan, Chaohui Zhan, Bo Gu, Yuntian Liu, Tong Wu, Yantao Qin, Mingpu Lv, Dingshun Xiang, Tao |
| contents | We introduce Neural Tensor Network States ($ν$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $ν$TNS framework, a neural network serves as a disentangler of the wave-function, transforming the physical degrees of freedom into renormalized variables with much less entanglement. The renormalized state is then efficiently encoded by a back-flow tensor network. This construction yields a compact yet highly expressive representation of strongly correlated quantum states. Using convolutional neural networks combined with matrix product states as a concrete implementation, we obtain state-of-the-art variational energies for the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice at the highly frustrated point $J_2/J_1=0.5$, for systems up to $20\times 20$ with periodic boundary conditions. Finite-size scaling of spin, dimer, and plaquette correlations exhibits power-law decay without magnetic or valence-bond long-range order, consistent with a gapless quantum spin-liquid ground state at that point.This $ν$TNS framework is flexible and naturally extensible to other neural and tensor-network structures, offering a general platform for investigating strongly correlated quantum many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14425 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Disentangling Tensor Network States with Deep Neural Network Fan, Chaohui Zhan, Bo Gu, Yuntian Liu, Tong Wu, Yantao Qin, Mingpu Lv, Dingshun Xiang, Tao Strongly Correlated Electrons Quantum Physics We introduce Neural Tensor Network States ($ν$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $ν$TNS framework, a neural network serves as a disentangler of the wave-function, transforming the physical degrees of freedom into renormalized variables with much less entanglement. The renormalized state is then efficiently encoded by a back-flow tensor network. This construction yields a compact yet highly expressive representation of strongly correlated quantum states. Using convolutional neural networks combined with matrix product states as a concrete implementation, we obtain state-of-the-art variational energies for the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice at the highly frustrated point $J_2/J_1=0.5$, for systems up to $20\times 20$ with periodic boundary conditions. Finite-size scaling of spin, dimer, and plaquette correlations exhibits power-law decay without magnetic or valence-bond long-range order, consistent with a gapless quantum spin-liquid ground state at that point.This $ν$TNS framework is flexible and naturally extensible to other neural and tensor-network structures, offering a general platform for investigating strongly correlated quantum many-body systems. |
| title | Disentangling Tensor Network States with Deep Neural Network |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2603.14425 |