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

TL;DR

This paper introduces SineKAN, a neural network ansatz based on Kolmogorov-Arnold Networks, which effectively models quantum many-body ground states and outperforms existing neural quantum state approaches in accuracy and efficiency.

Contribution

The paper proposes SineKAN, a novel neural quantum state ansatz using Kolmogorov-Arnold Networks with learnable sinusoidal activations, demonstrating superior performance in modeling quantum spin systems.

Findings

SineKAN accurately captures ground states of various quantum models.

SineKAN outperforms RBMs, LSTMs, and MLPs in the $J_1-J_2$ model.

SineKAN achieves high precision with minimal computational cost.

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.