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 $\mathtt{\text{SineKAN}}$, a NQS $\mathit{\text{ansatz}}$ based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that $\mathtt{\text{SineKAN}}$ 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 $\mathtt{\text{SineKAN}}$ model outperforms several previously explored neural quantum state $\mathit{\text{ans}}\ddot{\mathit{\text{a}}}\mathit{\text{tze}}$, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) $\mathit{\text{a.k.a.}}$ Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that $\mathtt{\text{SineKAN}}$ models can be trained to high precisions and accuracies with minimal computational costs.