Unsupervised learning of interacting topological phases from experimental observables.

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Machine Learning Applications

Background:

• Classifying topological phases of matter, especially those with strong interactions, is a significant challenge in condensed matter physics.
• Existing methods often require a priori knowledge or computationally expensive Hamiltonian diagonalization.

Purpose of the Study:

• To propose and validate an unsupervised machine learning approach for classifying symmetry-protected interacting topological phases.
• To enable classification directly from experimental observables without prior knowledge of the system's Hamiltonian.

Main Methods:

• Utilizing Green's functions, derived from experimentally measurable spectral functions, as input data for a diffusion map-based machine learning model.
• Demonstrating the approach on a one-dimensional interacting topological insulator model through extensive numerical simulations.
• Proposing a generic scheme for measuring spectral functions in ultracold atomic systems via momentum-resolved Raman spectroscopy.

Main Results:

• The diffusion map approach successfully classifies interacting topological phases in the studied model.
• The method effectively uses spectral functions as input, bypassing the need for Hamiltonian diagonalization.
• A practical experimental protocol for spectral function measurement in ultracold atoms is presented.

Conclusions:

• The proposed unsupervised machine learning method offers a versatile and autonomous protocol for identifying interacting topological phases.
• This approach significantly simplifies the characterization of complex topological materials from experimental data.
• The work paves the way for broader applications of machine learning in topological phase discovery.