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

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 textttSineKAN, a NQS textitansatz based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that textttSineKAN 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 J1-J2 model with different chain lengths. In our study of the J1-J2 model with L=100 sites, we find that the textttSineKAN model outperforms several previously explored neural quantum state textitans"atze, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) textita.k.a. Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that textttSineKAN models can be trained to high precisions and accuracies with minimal computational costs.