Machine learning phases of matter (1605.01735v1)

Abstract: Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network can be trained to detect multiple types of order parameter directly from raw state configurations sampled with Monte Carlo. In addition, they can detect highly non-trivial states such as Coulomb phases, and if modified to a convolutional neural network, topological phases with no conventional order parameter. We show that this classification occurs within the neural network without knowledge of the Hamiltonian or even the general locality of interactions. These results demonstrate the power of machine learning as a basic research tool in the field of condensed matter and statistical physics.

• The paper demonstrates the effective use of neural networks to identify phase transitions in models like the Ising model using Monte Carlo sampled configurations.
• The paper shows that both fully-connected and convolutional neural networks achieve up to 99% accuracy in detecting conventional and topological orders without prior Hamiltonian knowledge.
• The paper highlights machine learning's potential to tackle challenges in disordered systems and quantum state representation, paving the way for future experimental and theoretical breakthroughs.

An Expert Overview of "Machine Learning Phases of Matter"

The paper "Machine learning phases of matter" by Juan Carrasquilla and Roger G. Melko presents a methodological exploration of leveraging ML, particularly neural networks (NNs), to identify phases and phase transitions in condensed matter systems. The examination is grounded in the context of applying supervised learning to configurations derived from Monte Carlo sampling, aimed at discerning multiple types of order parameters.

Key Highlights and Methodology

The authors illustrate the applicability of neural networks—both fully-connected feed-forward NNs and convolutional neural networks (CNNs)—to classify phases in systems characterized by complexity analogous to that seen in machine learning challenges like image and natural language processing. Uniquely, the neural networks perform this classification task without prior knowledge of the Hamiltonian governing the system or the specific locality of interactions.

Theoretical and Methodological Approach

1. Supervised Learning for Phases and Transitions: The baseline experimental setup uses supervised machine learning to differentiate between low and high-temperature states across several prototypical models such as the ferromagnetic Ising model. The authors utilize TensorFlow for implementing the NNs and train them using Monte Carlo sampled configurations.
2. Neural Networks and Order Parameters: The paper establishes that fully-connected NNs efficiently detect conventional order parameters, akin to the bulk polarization in the Ising model. Through a detailed examination, the neural networks demonstrate accuracy rates of up to 99% in detecting transitions, which is validated against known phase transition temperatures.
3. Convolutional Neural Networks for Topological Phases: CNNs are extended to more complex disordered and topological phases like the Ising lattice gauge theory and Coulomb phases. The CNNs demonstrate the capability to handle these more nuanced states, absent any direct order parameter, by focusing on local constraints characteristic to the particular system phases.

Numerical Results and Implications

The authors provide concrete numerical evaluations and illustrate the learning paradigms using graphical snapshots of configurations across various setups. These insights reveal that while traditional Monte Carlo simulations directly measure order parameters, neural network approaches offer flexibility by potentially adapting to various unknown configurations without pre-specified considerations.

Implications and Future Directions

1. Application in Disordered Systems: The use of machine learning to interpret non-trivial states of matter, which lack standard order parameters, is particularly impactful. This could lead to new discoveries in systems where classical simulators struggle, such as those affected by the notorious Monte Carlo sign problem.
2. Quantum Information and State Representation: The paper posits that neural networks might be adapted to encode quantum states accurately, suggesting applications in quantum error correction and state tomography. Such prospects are essential in advancing quantum computational methods.
3. Generalization and Practical Viability: The ability of neural networks to generalize beyond their initial design is emphasized. This characteristic unlocks potential across different lattice structures, coupling types, and broader condensed matter systems, indicating the versatility of ML methods in overcoming challenges posed by complex physical systems.

In conclusion, Carrasquilla and Melko's research underscores the burgeoning role of machine learning as a tool for exploration within condensed matter physics, offering a complementary perspective to traditional methods with implications poised to influence future experimental and theoretical pursuits. The validation of machine learning in complex systems marks a pivotal step towards broader adoption in physics research, opening avenues for discovery in unexplored domains and aligning with the evolving capabilities of computational technologies.