Success by confusion

Discriminating gases from liquids or solids marked the origin of modern statistical mechanics. We have many excellent tools, both theoretical and experimental, to discern and characterize different phases. However, we still fail in the description of more complex systems such as high-temperature superconductors or certain quantum spin-liquids. Hence, we might profit from a new angle, a new approach, of how to identify phases and transitions between them.

In our recent publication, we used an artificial neural net to discriminate between different thermodynamic phases of quantum many-body systems. We generated numerical data representing the quantum phases. We then asked the neural net to group the data into two classes where we proposed an arbitrary phase-boundary. When the proposed boundary is coinciding with a true phase boundary, the performance of the network in assigning the labels is optimal. It is like trying to train a network to distinguish between cats and dogs. If you don’t confuse the network by training it with pictures of dogs while telling the net it looks at a cat, the performance will be best. Choosing a wrong phase boundary, is exactly such a confusion.

With this approach, we could detect phase transitions in a topological superconductor, in a many-body localized system of quantum spins as well as in the Haldane spin-1 chain without any human interaction. We believe that further refinements of our method will enable us to make progress on disordered spin systems and strongly correlated electron systems where we do not have a good physical understanding to date.