Machine Learning and Deep Learning in Quantum Materials: Symmetry, Topology, and the Rise of Altermagnets

Original Abstract

The landscape of condensed matter physics is facing an unprecedented data surge driven by high-throughput ab initio workflows and rapidly expanding experimental datasets. Traditional first-principles methods such as Density Functional Theory (DFT), despite their foundational role, suffer from cubic scaling, creating a major bottleneck when exploring the vast chemical space of quantum materials. This review analyzes how Machine Learning (ML) and Deep Learning (DL) are overcoming these limitations and accelerating the discovery of exotic phases of matter. We examine the shift from rigid descriptor-based models to flexible, symmetry-aware architectures, particularly E(3)-equivariant Graph Neural Networks (GNNs) that respect rotational and translational invariance. A central focus is the automated identification of topological phases, where ML models exploit symmetry indicators and elementary band representations to diagnose non-trivial topology without costly band structure integrations. The discussion culminates in a case study of the Altermagnet, a recently identified third class of magnetism beyond the ferromagnetic, antiferromagnetic dichotomy. We highlight how specialized AI search engines, combining graph theory with crystallographic symmetry analysis, have uncovered d-wave, g-wave, and even i-wave altermagnets, expanding the known landscape of magnetic order. The review concludes by addressing the interpretability gap and advocates for symbolic regression and active-learning frameworks to connect black-box predictions with experimentally verifiable mechanisms.