Speaker
Description
Localization in quantum systems is most commonly associated with disorder: Anderson's seminal result established that quenched randomness in a lattice potential suppresses diffusive transport through destructive interference, a mechanism subsequently extended to the interacting regime by many-body localization theory. Yet localization can emerge in perfectly ordered, translationally symmetric systems when the spectral geometry of the Hamiltonian enforces it---a phenomenon now recognized as disorder-free localization. We begin this talk with an introduction to this mechanism, tracing its appearance across several physical settings: lattice gauge theories with conserved local charges, flat-band systems with macroscopic ground-state degeneracy, and continuous-time quantum walks on fully connected graphs, where maximal connectivity paradoxically confines rather than delocalizes.
We focus on the last of these as a concrete and computationally tractable model. We present an efficient quantum circuit implementation of continuous-time quantum walks that produces disorder-free localization on random graphs from near-full to full connectivity. We then show that localization in this setting can be systematically destroyed by introducing disorder, and that this destruction is controllable. This controllability turns out to be precisely the resource needed to construct quantum batteries from such systems, where disorder acts as a tunable charging mechanism with favorable energetic cost relative to stored ergotropy.