Trapped Fermions Through Kolmogorov-Arnold Wavefunctions

TL;DR

This paper introduces a variational Monte Carlo approach using Kolmogorov-Arnold networks to accurately model trapped one-dimensional fermionic systems, capturing pairing effects and enabling efficient transfer learning.

Contribution

It develops a neural-network wavefunction ansatz with systematic transfer learning and incorporates short-distance behavior to improve efficiency and accuracy.

Findings

Achieves sub-percent precision against exact results.

Captures pairing effects in attractive interactions.

Enables efficient transfer learning with neural networks.

Abstract

We investigate a variational Monte Carlo framework for trapped one-dimensional mixture of spin-$\frac{1}{2}$ fermions using Kolmogorov-Arnold networks (KANs) to construct universal neural-network wavefunction ans\"atze. The method can, in principle, achieve arbitrary accuracy, limited only by the Monte Carlo sampling and was checked against exact results at sub-percent precision. For attractive interactions, it captures pairing effects, and in the impurity case it agrees with known results. We present a method of systematic transfer learning in the number of network parameters, allowing for efficient training for a target precision. We vastly increase the efficiency of the method by incorporating the short-distance behavior of the wavefunction into the ans\"atz without biasing the method.