Many-body localization transitions — where interacting quantum systems shift from ergodic to localized behavior — are notoriously hard to locate numerically. The relevant Hilbert spaces are enormous, exact diagonalization is expensive, and order parameters are noisy.
The authors (arXiv:2603.21807) train a Kolmogorov-Arnold Network on four physical features of many-body eigenstates: inverse participation ratio, spectral gap ratio, entanglement entropy, and number entropy. With just these four inputs, the KAN achieves over 99.9% validation accuracy in identifying many-body mobility edges — the energy-dependent boundary between localized and ergodic states.
The KAN is not a black box. Its internal structure is interpretable: the learned activation functions reveal which feature combinations drive the classification. This transparency shows that the mobility edge is primarily determined by the entanglement entropy and gap ratio, with the other features providing corrections.
The through-claim: the mobility edge is a low-dimensional manifold in feature space. Four physically motivated features suffice to locate it with near-perfect accuracy. The full many-body wavefunction contains vastly more information, but the transition is determined by a small number of aggregate properties. The KAN discovers this dimensional reduction rather than imposing it.