Oral: Gaussian Process Active Learning for 5-Parameter Heisenberg Hamiltonian Phase Diagram

We present an active learning-based Gaussian Process Classification scheme to efficiently map a multidimensional phase diagram of a J1-J2-J3 classical Heisenberg Hamiltonian in the presence of an external magnetic field H and anisotropy A. We use a variational minimization method to determine the lowest energy magnetic state for a given set of parameters of the Heisenberg model. By employing a Gaussian Process Classifier method along with straightforward margin sampling and Voronoi-based nearest-neighbor logic to quantify the uncertainty of the classifier, we find that it is possible to accurately map the phase diagram of the Heisenberg Hamiltonian by performing less number of variational minimizations compared to the conventional grid-based and random sampling methods. We quantify our results by a number of metrics, including Zero-One Loss, Log Loss, and our own metric to measure the accuracy of the phase boundary. Thus we use these constructed multi-dimensional phase diagrams to learn about the existence and nature of non-trivial and topological magnetic states.