(Part 1) The universal spectral-form-factor for MBL: Spectral correlations have emerged as a powerful probe to understand non-equilibrium physics, especially thermalization and quantum chaos. Chaotic systems have recently been shown to exhibit universal signatures in their so-called spectral form (SFF) factor, which are reproduced by random matrix ensembles, such as a 'linear ramp'. I will present an equivalent universal SFF for the many-body-localization (MBL) phase, distinct from quantum chaos, that can be exactly derived and checked by numerics.
(Part 2) A Z2 gauge theoretic approach to deconfined quantum criticality: Models of quantum spins are known to exhibit a rich variety of phases ranging from spin liquids to magnetic order. Some exotic phase transitions cannot be described by Ginzburg-Landau theory of order parameters and need additional ingredients like gauge fields. I will show that a certain class of such deconfined quantum critical phase diagrams can be efficiently modeled using Z2 gauge fields coupled to appropriate Higgs fields. These are applicable to physical systems ranging from quantum antiferromagnets to boundaries of topological insulators.