Machine Learning Entanglement Structure of Disordered Topological Phases and Competing Orders*

The entanglement spectrum is expected to provide a characterization of topologically ordered systems beyond traditional order parameters. Nevertheless, so far attempts at accessing this information relied on the presence of translational symmetry. Here we introduce a framework for using a simple artificial neural network (ANN) to detect defining features of a fractional quantum Hall state, a charge density wave state and a localized state from entanglement spectra, even in the presence of disorder. We then successfully obtain a phase diagram for Coulomb-interacting electrons at fractional filling \nu = 1/3, perturbed by modified interactions and disorder. Our results bench-mark well against existing measures in parts of the phase space where such measures are available. Hence we explicitly establish a finite region of robust topological order. Moreover, we establish that the ANN can indeed access and learn defining traits of topological as well as broken symmetry phases using only the entanglement spectra of ground states as input.