Engineering Topological Phases Guided by Statistical and Machine Learning Methods

TL;DR

This paper introduces a statistical and machine learning approach to identify topological phases in lattice models without prior phase diagram knowledge, successfully predicting the Haldane model as a proof of concept.

Contribution

A novel systematic method combining statistical sampling and machine learning to construct topological models from generic lattice data.

Findings

Marginal parameter distributions define topological models.

Parameter correlations contain hidden topological information.

Method successfully predicts the Haldane model for honeycomb lattices.

Abstract

The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. By sampling tight-binding parameter vectors from a random distribution we obtain data sets that we label with the corresponding topological index. This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values. We find that the marginal distributions of the parameters already define a topological model. Additional information is hidden in correlations between parameters. Here we present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A. The algorithm is straightforwardly applicable to any other AZ class or lattice and could be generalized to interacting systems.