Neural quantum states (NQSs) are a class of variational wave functions parametrized by neural networks to study quantum many-body systems. In this work, we propose SineKAN, a NQS ansatz based on Kolmogorov-Arnold networks, to represent quantum mechanical wave functions as nested univariate functions. We show that a SineKAN wave function 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. Beyond one dimension, we further demonstrate that SineKAN, augmented with a minimal reflection symmetry (rSineKAN), accurately describes the ground states of square-lattice systems, including the transverse-field Ising model and the antiferromagnetic Heisenberg model. In our study of the $J_1-J_2$ model with $L=100$ sites, we find that the SineKAN model outperforms several previously explored neural quantum state ansätze, including restricted Boltzmann machines, long short-term memory models, and multilayer perceptrons, aka feed forward neural networks, when compared to the results obtained from the density matrix renormalization group algorithm. We find that SineKAN models can be trained to high precision and accuracy with minimal computational costs.

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• Approximation methods for many-body systems
• Monte Carlo methods
• Quantum spin chains
• Spin lattice models
• Trial wave functions