Quantum Loop Topography for Machine Learning Transport

Despite the rapidly growing interest in harnessing machine learning in the study of quantum many-body systems, there remains a central challenge in efficiently extracting information from the model simulations of the quantum states and turning the information into formats compatible with the machine learning architecture, such as an artificial neural network. Here we introduce quantum loop topography (QLT): a feature-selection machine learning procedure by evaluating correlators’ loop products of the microscopic models at independent Monte Carlo steps. Following the contribution of the current-current correlations, we demonstrate that QLT can probe the distinctive transport properties of diverse states of matter, which are sometimes challenging to access directly. To showcase this approach, we study the emergent superconducting fluctuations as well as the topological phases with quantized Hall transport. We find that the QLT approach detects a change in transport in very good agreement with their established phase diagrams. We also demonstrate that our pre-selection of features relevant to transport allows us to work with a simple neural network, and then offer an interpretation of such a neural network for the analytical decision criteria. The high fidelity and numerical efficiency of our machine learning algorithm also point a way to identify hitherto elusive transport phenomena such as the non-Fermi liquids.