Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States

• URL: http://arxiv.org/abs/2506.01891v4
• Date: Fri, 27 Jun 2025 21:50:31 GMT
• Title: Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States
• Authors: Mahmud Ashraf Shamim, Eric A F Reinhardt, Talal Ahmed Chowdhury, Sergei Gleyzer, Paulo T Araujo,
• Abstract summary: We propose textttSineKAN, a neural network model to represent quantum mechanical wave functions.<n>We find that textttSineKAN models can be trained to high precisions and accuracies with minimal computational costs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural Quantum States (NQS) are a class of variational wave functions parametrized by neural networks (NNs) to study quantum many-body systems. In this work, we propose \texttt{SineKAN}, a NQS \textit{ansatz} based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that \texttt{SineKAN} wavefunction with learnable sinusoidal activation functions can capture the ground state energies, fidelities and various correlation functions of the one dimensional Transverse-Field Ising model, Anisotropic Heisenberg model, and Antiferromagnetic $J_{1}-J_{2}$ model with different chain lengths. In our study of the $J_1-J_2$ model with $L=100$ sites, we find that the \texttt{SineKAN} model outperforms several previously explored neural quantum state \textit{ans\"atze}, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) \textit{a.k.a.} Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that \texttt{SineKAN} models can be trained to high precisions and accuracies with minimal computational costs.

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