Machine Learning Phases of Strongly Correlated Fermions (1609.02552v3)

Abstract: Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling). We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling. This transfer learning approach predicts that the instability to the magnetic phase extends to at least 5% doping in this region. Our results pave the way for other machine learning applications in correlated quantum many-body systems.

• The paper demonstrates that a tailored 3D CNN accurately identifies finite-temperature magnetic phase transitions in the Hubbard model.
• It leverages quantum Monte Carlo simulations combined with neural architectures adapted from human action recognition to analyze auxiliary field configurations.
• The results show robust predictions of magnetic order at half-filling and up to 5% doping, underscoring the potential of machine learning in quantum many-body studies.

Overview of "Machine Learning Phases of Strongly Correlated Fermions"

The paper presented by Kelvin Ch'ng, Juan Carrasquilla, Roger G. Melko, and Ehsan Khatami offers a significant application of machine learning methods to condensed matter physics, notably focusing on strongly correlated fermions. The research deploys a convolutional neural network (CNN) to identify finite-temperature phases within the Hubbard model, showcasing how machine learning can advance our understanding and predictive capabilities in many-body quantum systems.

Core Methodology

This paper leverages a three-dimensional CNN trained on data generated via quantum Monte Carlo simulations of the Hubbard model, specifically targeting the characterization of magnetic phases at finite temperatures. The authors structured their CNN to utilize auxiliary field configurations as input, which incorporate both spatial and imaginary time components. This model is particularly adapted from frameworks used for human action recognition, emphasizing the versatility of such neural approaches.

Results

The CNN successfully delineates the transition temperature for the magnetic phase diagram at half filling, with results indicating its reliability even at small lattice sizes. By training the network with half-filled configurations, it precisely predicts the trend in transition temperature as the system undergoes doping, which extends its magnetic phase instability to at least 5% doping from half-filling.

Notable findings include the following:

• The CNN model provides an accurate mapping of the N\textsubscript{e}el transition temperature across varying interaction strengths, up to $U = 16$.
• With doping away from half-filling, the network predicts magnetic order persistence, revealing the robustness of the phase transition predictions under these conditions.

Implications and Future Directions

The implications of this work are profound, offering a novel method for analyzing phases in complex quantum many-body systems using machine learning. The utilization of trained networks for predicting unknown phase diagrams underscores their potential in quantum physics applications where traditional methods face computation and scalability limits.

The paper also provides a basis for future investigations which could focus on:

• Expanding the applicability of trained networks to other quantum systems affected by the notorious 'sign problem.'
• Integrating this methodology with unsupervised learning techniques for deeper exploration of phase transitions.

This paper demonstrates the viability of neural networks as tools in quantum material studies, suggesting further exploration of learning frameworks tailored to specific physical phenomena.