Unsupervised Learning of Non-Hermitian Topological Phases.

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Machine Learning Applications

Background:

• Non-Hermitian topological phases exhibit unique phenomena like the non-Hermitian skin effect.
• Conventional methods for classifying Hermitian topological phases are insufficient for non-Hermitian systems.
• The breakdown of bulk-boundary correspondence complicates analysis in non-Hermitian systems.

Purpose of the Study:

• To develop an unsupervised machine learning approach for classifying non-Hermitian topological phases.
• To address the challenges posed by the non-Hermitian skin effect in machine learning classification.
• To provide a robust method for identifying topological phases in non-Hermitian systems.

Main Methods:

• Utilized diffusion maps, a manifold learning technique, for unsupervised classification.
• Investigated the impact of the non-Hermitian skin effect on clustering algorithms.
• Employed theoretical analysis and numerical simulations on two prototypical models.

Main Results:

• Demonstrated that the non-Hermitian skin effect obstructs direct application of existing unsupervised learning methods.
• Identified that using "on-site" elements of the projective matrix as input data effectively circumvents classification challenges.
• Successfully clustered non-Hermitian topological phases using the proposed approach.

Conclusions:

• The developed unsupervised machine learning strategy offers a viable path for classifying non-Hermitian topological phases.
• The findings provide crucial guidance for future theoretical and experimental research in this domain.
• This work paves the way for broader applications of machine learning in studying complex quantum systems.