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Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
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Automatic learning of topological phase boundaries.

Alexander Kerr1, Geo Jose1, Colin Riggert1

  • 1Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, 440 W. Brooks St., Norman, Oklahoma 73019, USA and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA.

Physical Review. E
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Summary

Machine learning now identifies topological phase transitions without manual tuning. A new heuristic automatically finds optimal parameters for diffusion maps, simplifying the analysis of complex quantum systems.

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Area of Science:

  • Condensed matter physics
  • Machine learning
  • Quantum mechanics

Background:

  • Topological phase transitions deviate from Landau's symmetry breaking model.
  • Identifying these transitions is challenging due to global topological indices.
  • Diffusion maps offer a promising approach but require hyperparameter tuning.

Purpose of the Study:

  • To develop a machine learning heuristic for automated identification of topological phase transitions.
  • To eliminate the need for manual hyperparameter adjustment in diffusion map analysis.
  • To accurately generate phase diagrams for various physical models.

Main Methods:

  • Introduction of a novel heuristic for automated hyperparameter selection in diffusion maps.
  • Application of the heuristic to analyze three distinct physical models.
  • Generation of phase diagrams directly from model parameters without user intervention.

Main Results:

  • The heuristic successfully identified topological phase transitions across all tested models.
  • Accurate phase diagrams were generated automatically, demonstrating the method's efficacy.
  • The need for manual tuning of data length scale and phase boundary number was eliminated.

Conclusions:

  • The proposed heuristic provides an automated and user-independent method for analyzing topological phase transitions.
  • This advancement simplifies the application of diffusion maps in condensed matter physics research.
  • The approach enables efficient and accurate phase diagram generation for complex quantum systems.