Deep Learning Hamiltonians from Disordered Image Data in Quantum Materials

Current advancements in surface probes have allowed researchers to have a large availability of images of quantum materials over different lengths and time scales. Those images have revealed the formation of intricate patterns as some materials approach criticality. In such cases, the spatial structure should encode information about interactions, dimensionality, and disorder – a spatial encoding of the Hamiltonian driving the pattern formation. With the well-known capabilities of deep learning techniques for image recognition, we have developed a framework to recognize the underlying physics that best describes the complex pattern formation in a film of VO₂ during the metal-to-insulator transition. In this talk, we will go through the steps in developing the deep learning model: the selection of the Hamiltonians and the patterns they form, the data preparation, and the multi-label classification of images using a Convolutional Neural Network. We then vet this procedure using SNIM maps. Finally, we apply this method to new optical microscopy maps. Using our results, we propose a new machine learning based criterion for diagnosing a physical system’s proximity to criticality.