We show that a simple artificial neural network trained on entanglement
spectra of individual states of a many-body quantum system can be used to
determine the transition between a many-body localized and a thermalizing
regime. Specifically, we study the Heisenberg spin-1/2 chain in a random
external field. We employ a multilayer perceptron with a single hidden layer,
which is trained on labeled entanglement spectra pertaining to the fully
localized and fully thermal regimes. We then apply this network to classify
spectra belonging to states in the transition region. For training, we use a
cost function that contains, in addition to the usual error and regularization
parts, a term that favors a confident classification of the transition region
states. The resulting phase diagram is in good agreement with the one obtained
by more conventional methods and can be computed for small systems. In
particular, the neural network outperforms conventional methods in classifying
individual eigenstates pertaining to a single disorder realization. It allows
us to map out the structure of these eigenstates across the transition with
spatial resolution. Furthermore, we analyze the network operation using the
dreaming technique to show that the neural network correctly learns by itself
the power-law structure of the entanglement spectra in the many-body localized
regime.Comment: 12 pages, 10 figure
