Learning what a machine learns in a many-body localization transition.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Machine Learning Applications

Background:

• Disordered interacting systems exhibit complex phases like many-body localization (MBL) and thermal phases.
• Identifying these phases typically requires analyzing the system's energy spectrum.
• Machine learning offers novel approaches to analyze complex physical phenomena.

Purpose of the Study:

• To investigate how convolutional neural networks (CNNs) identify distinct phases in random spin systems.
• To understand the specific features CNNs utilize for phase identification.
• To develop new diagnostics for phase transitions in disordered systems.

Main Methods:

• Utilized a convolutional neural network (CNN) trained on normalized energy spectra of random spin systems.
• Analyzed the network's feature selection at the smallest nontrivial kernel width.
• Examined network performance with increased kernel widths.

Main Results:

• The CNN with the smallest kernel width identified level spacing as the key feature distinguishing the many-body localized phase from the thermal phase.
• Increasing the kernel width revealed an alternative diagnostic for phase detection directly from the energy spectrum.
• The study demonstrates CNNs can uncover unique physical signatures in complex quantum systems.

Conclusions:

• Convolutional neural networks can effectively distinguish between many-body localized and thermal phases in disordered spin systems.
• Network architecture, specifically kernel width, influences the identified distinguishing features.
• This work provides a new machine learning-driven approach for analyzing quantum phase transitions.