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We apply support vector machine (SVM) to study the phase transition betweenmany-body localized and thermal phases in a disordered quantum Ising chain in atransverse external field. The many-body eigenstate energy $E$ is bounded by abandwidth $W=E_{max}-E_{min}$. The transition takes place on a phase diagramspanned by the energy density $\epsilon=2(E-E_{min})/W$ and the disorderstrength $\delta J$ of the spin interaction uniformly distributed within$[-\delta J, \delta J]$, formally parallel to the mobility edge in Andersonlocalization. In our study we use the labeled probability density of eigenstatewavefunctions belonging to the deeply localized and thermal regimes at twodifferent energy densities ($\epsilon$'s) as the training set, i.e., providinglabeled data at four corners of the phase diagram. Then we employ the trainedSVM to predict the whole phase diagram. The obtained phase boundaryqualitatively agrees with previous work using entanglement entropy tocharacterize these two phases. We further analyze the decision function of theSVM to interpret its physical meaning and find that it is analogous to theinverse participation ratio in configuration space. Our findings demonstratethe ability of the SVM to capture potential quantities that may characterizethe many-body localization phase transition.

Interpretable Machine Learning Study of Many-Body Localization Transition in Disordered Quantum Ising Spin Chains