Machine learning phases of matter

Condensed-matter physics is the study of the collective behaviour of infinitely complex assemblies of electrons, nuclei, magnetic moments, atoms or qubits(1). This complexity is reflected in the size of the state space, which grows exponentially with the number of particles, reminiscent of the 'curse of dimensionality' commonly encountered in machine learning(2). Despite this curse, the machine learning community has developed techniques with remarkable abilities to recognize, classify, and characterize complex sets of data. Here, we showthat modern machine learning architectures, such as fully connected and convolutional neural networks(3), can identify phases and phase transitions in a variety of condensed-matter Hamiltonians. Readily programmable through modern software libraries(4,5), neural networks can be trained to detect multiple types of order parameter, as well as highly non-trivial states with no conventional order, directly from raw state configurations sampled with Monte Carlo(6,7).