Group-equivariant autoencoder for identifying spontaneously broken symmetries.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Machine Learning

Background:

• Phase transitions are characterized by changes in system symmetry.
• Identifying these symmetry changes is crucial for understanding material properties.
• Current methods for detecting phase transitions can be computationally intensive and less accurate.

Purpose of the Study:

• To introduce a novel deep neural network (DNN) method, the group-equivariant autoencoder (GE autoencoder), for identifying phase boundaries.
• To leverage group theory to constrain the autoencoder and learn symmetry-invariant order parameters.
• To improve the accuracy, robustness, and efficiency of phase transition detection.

Main Methods:

• Utilized group theory to identify invariant symmetries and constrain the GE autoencoder's parameters.
• Incorporated symmetry regularization terms into the loss function for learned order parameter equivariance.
• Applied the GE autoencoder to 2D classical ferromagnetic and antiferromagnetic Ising models.

Main Results:

• The GE autoencoder accurately determined which symmetries spontaneously broke at different temperatures.
• It estimated critical temperatures in the thermodynamic limit with higher accuracy, robustness, and time efficiency compared to a baseline autoencoder.
• The method demonstrated greater sensitivity in detecting external symmetry-breaking magnetic fields.

Conclusions:

• The GE autoencoder provides a powerful and efficient tool for detecting phase transitions and analyzing spontaneous symmetry breaking.
• This DNN approach offers significant advantages over traditional methods in terms of accuracy and computational performance.
• The framework is adaptable for studying various physical systems exhibiting phase transitions and symmetry changes.