Disentangling Tensor Network States with Deep Neural Network

• URL: http://arxiv.org/abs/2603.14425v1
• Date: Sun, 15 Mar 2026 15:09:00 GMT
• Title: Disentangling Tensor Network States with Deep Neural Network
• Abstract summary: We introduce a variational wave-function ansatz that integrates deep neural networks with tensor-network architectures.<n>In the $$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.<n>This construction yields a compact yet highly expressive representation of strongly correlated quantum states.
• Score: 20.1390115178447
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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