Machine assisted identification of unconventional order and ground-state selection in a breathing pyrochlore magnet

Machine-learning is drawing enormous attention in physics and has proven useful for sovling various physical problems. However, there are still very few instances of such techniques being applied to hard problems and providing new insights. In this work, we apply the tensorial-kernel support-vector-machine (TK-SVM) method to a classical anti-ferromagnet with Dzyaloshinskii–Moriya interaction on the breathing pyrochlore lattice, where we uncover the nature of the q = W phase below a rank-2 U(1) spin liquid found in PRL 124, 127203 (2020). Our machine identifies the previously unknown order parameter of this phase and the constraint that selects the ground states, whose construction is sufficiently intricate and was not realized using traditional methods.