Recent progress in quantum spin glasses

In this talk I will give an overview over recent results on mean-field spin-glass models with a transversal magnetic field.

For such models both thermodynamic quantities such as the free energy and its fluctuations, as well as spectral and localization properties of eigenvectors are of interest to a diverse list of communities. A full mathematical analysis of properties is completed for the simplest, yet ubiquitous quantum random energy model.

For models with a more complicated (classical) correlation structure such as the Sherrington-Kirkpatrick model, a more qualitative analysis proves the existence of a phase transition.