Revealing phase diagrams of quantum systems with optimal predictors

Neural networks (NNs) have been successfully used to determine phase diagrams from experimentally accessible data with little prior physical knowledge. Recently, we have replaced the NNs in several such phase classification methods for one-dimensional phase diagrams featuring two distinct phases of matter by optimal non-parametric predictive models [1]. These optimal predictors can be constructed based on the probability distributions underlying the physical system and capture the output of NNs in the limit of high model capacity without explicit training, which allows for a more efficient detection of phase transitions from data. Here, we extend this framework to higher-dimensional phase diagrams that may feature multiple distinct phases of matter. As an example, we map out the two-dimensional phase diagram of a quantum many-body system from numerical data.