Three-body renormalization group limit cycles based on unsupervised feature learning

TL;DR

This paper explores which two-body interactions lead to limit cycles in three-body systems at low energies using unsupervised feature learning and genetic algorithms, highlighting the inverse square potential as uniquely significant.

Contribution

It introduces a novel approach combining variational autoencoders and genetic algorithms to identify two-body potentials that induce three-body limit cycles without prior restrictions.

Findings

Inverse square potential uniquely minimizes the limit cycle loss

Unsupervised autoencoders effectively generate synthetic potentials

Genetic algorithm identifies key potentials inducing limit cycles

Abstract

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.