New insights into four-boson renormalization group limit cycles

TL;DR

This paper uses machine learning to explore how renormalization group limit cycles in three-boson systems extend to four-boson systems, revealing that four-body terms do not introduce new scales at low energy.

Contribution

It introduces a novel machine learning approach to verify the transfer of limit cycles from three- to four-boson systems and demonstrates the role of inverse-square potentials.

Findings

Limit cycles in four-boson systems are linked to those in three-boson systems.

Four-body terms do not generate additional low-energy scales.

Inverse-square potential is key to limit cycle behavior.

Abstract

Using machine learning techniques, we verify that the emergence of renormalization group limit cycles beyond the unitary limit is transferred from the three-boson subsystems to the whole four-boson system. Focussing on four identical bosons, we first generate populations of synthetic singular potentials within the latent space of a boosted ensemble of variational autoencoders. After introducing the limit cycle loss for measuring the deviation of a given renormalization group flow from limit cycle behavior, we minimize it by applying an elitist genetic algorithm to the generated populations. The fittest potentials are observed to accumulate around the inverse-square potential, which we prove to generate limit cycles for four bosons and which is already known to produce limit cycles in the three-boson system. This also indicates that a four-body term does not enter low-energy observables at leading order, since we do not observe any additional scale to emerge.