Measures of chaos for a minimal quantum glass model

An interesting feature of glasses is that they do not thermalize in a single step. The time it takes to thermalize within a subspace of the system's configuration space may be much shorter than the time needed to thermalize across the full space. This behavior is a result of high free energy barriers which divide the configuration space into sectors. We examine a generalization of the Rosenzweig-Porter model we term the "Block Rosenzweig-Porter" (BRP) model which has a simple sector structure. The simple structure allows for the calculation of measures of chaos such as the spectral form factor and the spectrum of fractal dimensions of the eigenstates. We present the results for these measures and discuss their relation to each other. We find that the BRP model can exhibit glassy behavior and discuss its relevance to other quantum glass models.