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Unsupervised Data-Driven Classification of Topological Gapped Systems with Symmetries.

Yang Long¹, Baile Zhang^1,2

¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.

Physical Review Letters

|February 10, 2023

Summary

Researchers developed a data-driven method to classify topological phases using machine learning, creating a topological periodic table without prior knowledge of invariants. This approach accounts for spatial symmetries and identifies new topological phases.

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Mechanics

Background:

The topological periodic table classifies gapped systems based on K theory, but lacks direct Hamiltonian-based methods.
Identifying topological phases often relies on trial-and-error checking of incomplete invariant lists.

Purpose of the Study:

To develop an unsupervised, data-driven approach for classifying topological gapped systems with symmetries.
To construct a topological periodic table using machine learning without a priori knowledge of topological invariants.

Main Methods:

Employed unsupervised machine learning algorithms for topological phase classification.
Integrated spatial symmetry considerations into the data-driven classification framework.

Main Results:

Successfully constructed a topological periodic table using a data-driven strategy.
Identified novel topological phases previously misclassified as trivial.
Demonstrated the ability to account for spatial symmetries in classification.

Conclusions:

Introduced machine learning to topological phase classification, enabling data-driven discovery.
Paved the way for intelligent exploration of new topological matter phases.
Provided a more robust and comprehensive method for topological phase identification.