Unsupervised identification of topological order using predictive models

TL;DR

This paper introduces an unsupervised machine learning approach using neural networks to identify topological phases and phase transitions in complex quantum and classical systems without prior knowledge.

Contribution

It demonstrates a novel method to detect topological phases and transitions using predictive models, applicable to systems lacking local order parameters.

Findings

Successfully identified topological phases in classical and quantum models

Predictive model accuracy correlates with phase transitions

Applicable to systems without local order parameters

Abstract

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 topological phases and transitions out of them. 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.