phase-of-matter-by-machine-learning

This project introduces unsupervised machine learning in the study of phase of matter in physics.

Symmetry broken phases

• Potts models(clock models) in square lattice. n=2 corresponds to Ising model.
• Monto Carlo method is used to simulate spin configurations at different temperatues.
• High dimensional data of spin configurations are reduced by PCA method.
• It is clear to see symmetric pattern after dimension reduction.
• Theory of symmetry broken phase may be formulated by unsupervised machine learning.

KT phase transition  

In XY model, different phases are not marked by symmetry breaking

• Traditional dimension reduction cannot tell KT phase transition
• Autoencoder method are used, including cnn, variational autoencoder(va), a combination of cnn and va.
• At this stage, cnn method wins. But it is still not good to reconstuct the right spin configuration with vortex.
• Further exploration is badly required. Autoencoder of topological objects such as vortex is not a topic of attention for the deep learning  community, but it seems not a trivial problem.