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Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers

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Published on: September 4, 2015

Unsupervised learning of interacting topological phases from experimental observables.

Li-Wei Yu^1,2, Shun-Yao Zhang², Pei-Xin Shen²

¹Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.

Fundamental Research

|December 11, 2024

Summary

We developed an unsupervised machine learning method to classify interacting topological phases using experimental data. This approach, based on diffusion maps and Green's functions, simplifies identifying complex topological materials.

Keywords:

Diffusion map Spectral function Topological phases Ultracold atom Unsupervised learning

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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.