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

We develop, train, and apply a support vector machine (SVM) to study the phase transition between many-body localized and thermal phases in a disordered quantum Ising chain. We use the labeled probability density of eigenstate wavefunctions in the deeply localized and thermal regimes at two different energy densities as the training set. We find that the trained SVM is then able to predict the whole phase diagram. The obtained phase boundary qualitatively agrees with previous work using entanglement entropy to characterize these two phases. We further analyze the decision function of the SVM to interpret its physical meaning and find that it is analogous to the inverse participation ratio in the many-body configuration space. Our findings demonstrate the ability of the SVM to capture potential quantities that may characterize the many-body localization phase transition. The qualitative agreement of phase boundary obtained by SVM and by scaling entanglement entropy motivates further exploration of the relation between these two different quantities in connection to many-body localization.