Learning phases with Quantum Monte Carlo simulation cell

We propose the use of the "spin-opstring", derived from Stochastic Series Expansion Quantum Monte Carlo (QMC) simulations as machine learning input data. It offers a compact, memory-efficient representation of QMC simulation cells, combining the initial state with an operator string that encodes the state's evolution through imaginary time. Using supervised machine learning, we demonstrate the input's effectiveness in capturing both conventional and topological phase transitions. Additionally, we conduct a regression task to predict superfluid density, which reflects non-local properties of the quantum system, and achieve good accuracy. We also demonstrate the capability of spin-opstring data in transfer learning by training models on one quantum system and successfully predicting on another, as well as showing that models trained on smaller system sizes generalize well to larger ones. Finally, using two state-of-the-art interpretability techniques, Layer-wise Relevance Propagation and SHapley Additive exPlanations, we show that the machine learning models learn and rely on physically meaningful features from the input data. Together, these findings establish the spin-opstring as a broadly-applicable and interpretable input format for machine learning in quantum many-body physics.