Quantum glasses through the lens of mean field models

The interplay of frustrated interactions, disorder, and quantum fluctuations can lead to transitions between ergodic phases and non-ergodic glassy behavior. These quantum glasses are receiving renewed attention in recent years due to their relevance in quantum annealing, as well as their potential use as quantum neural networks. Despite their fundamental importance, characterizing the glass transition and the properties of the glassy phase remains a challenging problem, still posing numerous open questions. In this talk, I will present recent numerically exact results for mean-field models, which shed light on the quantum dynamics and on the structure of collective excitations in the glassy phase. I will first focus on insulating mean-field glasses, describing local magnetic impurities subject to frustrated long-range interactions, and show that they share a universal form of low-energy excitations. I will then briefly comment on the effects of coupling the impurities to a metallic bath, and sketch preliminary findings and unresolved questions for the resulting metallic glasses.