Three-Phase Confusion Learning

Area of Science:

• Quantum Many-Body Theory
• Machine Learning Applications

Background:

• Neural Networks (NNs) are increasingly used in quantum many-body theory.
• Learning by Confusion (LbC) is an unbiased NN scheme for identifying equilibrium phase diagrams.
• Existing LbC methods are limited to systems with two phases.

Purpose of the Study:

• To generalize the Learning by Confusion scheme for quantum systems with more than two phases.
• To adapt NNs for detecting systems exhibiting three or more phases.

Main Methods:

• A generalized confusion scheme using a ternary Neural Network classifier.
• Testing the method on free and interacting Kitaev chains.
• Applying the method to the one-dimensional Extended Hubbard model.

Main Results:

• The generalized LbC scheme successfully identified phase diagrams in multi-phase systems.
• Achieved results consistent with previous studies.
• Demonstrated the effectiveness of ternary classifiers for multi-phase detection.

Conclusions:

• The generalized Learning by Confusion approach extends NN applications in quantum many-body physics.
• This work highlights the utility of machine learning for complex quantum system analysis.
• The method provides an unbiased route to discovering phase transitions.