Topological phase transitions

Identifying phase transitions is one of the key questions in theoretical and experimental condensed matter physics alike. Topological phase transitions represent an outstanding challenge, as they cannot be described by a local order parameter. In addition, tools developed to detect topological phase transitions as e.g. ground state degeneracy, topological entanglement entropy or the entanglement spectrum are not only demanding to compute but require knowledge that might not be experimentally accessible.
There is hence a strong demand to develop new probes to detect topological phase transitions. It is particularly useful to have access to a generic non-system specific probe, as e.g. the specific heat for thermal transitions.

In our work, we use a neural network based approach to detect phase transitions without local order parameter. The central idea of our approach is to distill a predictive model that relates input data from numerical or experimental studies to the output in the form of a known tuning parameter. We can then infer the position of the phase transition by analysing the network’s performance in predicting this parameter. We investigate two generic models hosting phase transitions without a local order parameter, the finite-temperature cross-over in Wegner’s Ising gauge theory and Kitaev’s toric code in the presence of disorder.