Three-body renormalization group limit cycles based on unsupervised feature learning
arXiv:2111.07820 · doi:10.1088/2632-2153/ac579b
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.
arXiv comment24 pages, 12 figures
References in corpus (18)
- Adam: A Method for Stochastic Optimization
- Auto-Encoding Variational Bayes
- Gaussian Error Linear Units (GELUs)
- Striving for Simplicity: The All Convolutional Net
- The information bottleneck method
- Universality in Few-body Systems with Large Scattering Length
- Evidence for Efimov quantum states in an ultracold gas of cesium atoms
- Renormalization of the Three-Body System with Short-Range Interactions
- Singular Potentials and Limit Cycles
- Efimov States in Nuclear and Particle Physics
- An Infrared Renormalization Group Limit Cycle in QCD
- The Renormalization Group Limit Cycle for the 1/r^2 Potential
- On the limit cycle for the 1/r^2 potential in momentum space
- Pion-mass dependence of three-nucleon observables
- More on the infrared renormalization group limit cycle in QCD
- Universality in few-body systems with large scattering length
- Renormalization Group Limit Cycle for Three-Stranded DNA
- An Infrared Renormalization Group Limit Cycle in QCD