Machine Learning Topological Invariants with Neural Networks.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Machine Learning Applications

Background:

• Topological band insulators possess unique properties characterized by topological invariants.
• Distinguishing topological phases typically requires analyzing global properties of Hamiltonians.
• Machine learning offers potential for analyzing complex quantum systems.

Purpose of the Study:

• To investigate the efficacy of supervised neural networks in classifying topological phases.
• To determine if neural networks can predict topological winding numbers accurately.
• To explore the interpretability of neural networks in understanding topological features.

Main Methods:

• Supervised training of neural networks using Hamiltonians of 1D insulators with chiral symmetry.
• Testing the trained network's predictive accuracy on Hamiltonians with varying winding numbers, including those outside the training set.
• Analyzing the internal structure of the neural network to understand learned features.

Main Results:

• The neural network achieved nearly 100% accuracy in predicting topological winding numbers.
• The network successfully generalized to predict winding numbers for Hamiltonians not encountered during training.
• Analysis confirmed the network learned a discrete version of the winding number formula.

Conclusions:

• Neural networks can effectively capture global and nonlinear topological features of quantum phases from local inputs.
• The study highlights the potential of machine learning for topological phase identification in condensed matter physics.
• Considerations regarding symmetry and regularization effects in machine learning for physics are noted.