Identifying Topological Phase Transitions in Experiments Using Manifold Learning.

Area of Science:

• Condensed Matter Physics
• Machine Learning
• Optical Systems

Background:

• Topological phase transitions are crucial in condensed matter physics, often characterized by edge states.
• Identifying these transitions experimentally typically requires comprehensive system data.

Purpose of the Study:

• To demonstrate a novel machine learning approach for identifying topological phase transitions from experimental data.
• To show the efficacy of diffusion maps in detecting these transitions even with incomplete data.

Main Methods:

• Utilized diffusion maps, a nonlocal unsupervised machine learning technique.
• Applied the method to experimental data from an optical system exhibiting a topological phase transition.

Main Results:

• Successfully identified topological phase transitions using diffusion maps.
• The approach accurately detected transitions even when data was limited to a small system portion.
• The method worked without requiring data on edge states.

Conclusions:

• Diffusion maps offer a powerful tool for identifying topological phase transitions from experimental data.
• This machine learning approach provides a robust method for analyzing complex physical systems.
• The technique's ability to work with partial data broadens its applicability in experimental physics.