Three-body renormalization group limit cycles based on unsupervised feature learning
This addresses a fundamental question in theoretical physics regarding limit cycles, but the approach is incremental as it applies existing machine learning methods to a specific domain.
The paper tackled the problem of identifying which two-body interactions cause renormalization group limit cycles in three-body systems at low energies, and found that the inverse square potential is the only one that minimizes the limit-cycle loss independent of hyperangle.
Both the three-body system and the inverse square potential carry a special significance in the study of renormalization group limit cycles. In this work, we pursue an exploratory approach and address the question which two-body interactions lead to limit cycles in the three-body system at low energies, without imposing any restrictions upon the scattering length. For this, we train a boosted ensemble of variational autoencoders, that not only provide a severe dimensionality reduction, but also allow to generate further synthetic potentials, which is an important prerequisite in order to efficiently search for limit cycles in low-dimensional latent space. We do so by applying an elitist genetic algorithm to a population of synthetic potentials that minimizes a specially defined limit-cycle-loss. The resulting fittest individuals suggest that the inverse square potential is the only two-body potential that minimizes this limit cycle loss independent of the hyperangle.