Compressing First-Principles Quantum Interactions in Materials via Decomposition and Tensor Learning

The microscopic interactions of electrons, phonons, and excitations in materials – also known as quantum interactions – are typically represented as dense matrices or high-dimensional tensors. With state-of-the-art first-principles methods, computing these interactions is prohibitively expensive for high-order processes and for materials with large unit cells, or in the common scenario where a high-resolution in momentum space is needed.

In this talk, I will discuss our recent progress on compressing first-principles quantum interactions using decomposition and tensor-learning techniques. I will show that these AI-based approaches enable speed-ups by two orders of magnitude for calculations of electron-phonon interactions and associated properties – such as electronic transport, relaxation times, superconducting Tc, polarons, etc. – and three orders of magnitude speed-ups for calculations of phonon-phonon interactions, thermal conductivities, and phonon scattering rates.

In addition to disruptively faster calculations of quantum interactions and material properties, these methods enable entirely new many-body calculations [3] and reveal the inherent low-rank character and compressibility of quantum interactions, providing a systematic approach for developing simplified Pareto-optimal models. I will conclude by describing our efforts to use tensor decomposition and learning to compute high-order quantum interactions that are currently inaccessible. This paradigm shift for quantitative studies of interactions in condensed matter, initiated in Refs. [1,2], is poised to chart a new direction in the field at the intersection of AI/machine learning and condensed matter physics.