Unsupervised identification of topological phase transitions using predictive models

• Published in: New journal of physics 2020-04, Vol.22 (4), p.45003
• Main Authors: Greplova, Eliska, Valenti, Agnes, Boschung, Gregor, Schäfer, Frank, Lörch, Niels, Huber, Sebastian D
• Format: Article
• Language: English
• Subjects: Broken symmetry; Gauge theory; Identification methods; Ising gauge theory; Ising model; Machine learning; Mathematical models; Model accuracy; Neural networks; Order parameters; Parameter identification; Phase transitions; Phases; Physics; Prediction models; quantum phase transitions; topological order; topological phase transitions; Topology; toric code; unsupervised learning
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ab7771

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior theoretical knowledge. While for phases characterized by a broken symmetry, the use of unsupervised methods has proven to be successful, topological phases without a local order parameter seem to be much harder to identify without supervision. Here, we use an unsupervised approach to identify boundaries of the topological phases. We train artificial neural nets to relate configurational data or measurement outcomes to quantities like temperature or tuning parameters in the Hamiltonian. The accuracy of these predictive models can then serve as an indicator for phase transitions. We successfully illustrate this approach on both the classical Ising gauge theory as well as on the quantum ground state of a generalized toric code.