Quantum Phases of a Strongly Disordered Two-Legged Josephson Ladder

Disordered superconductors in low dimensions provide an exemplary manifestation for the role of quantum fluctuations in a many-body system. Specifically in Josephson arrays with comparable Josephson and charging energies ($E_J\sim E_C$), disorder tends to change the nature of the paradigmatic Superconductor-Insulator Transition (SIT) and potentially leads to formation of multiple distinct phases. We address this problem in a model of a two-legged Josephson ladder subjected to a wide spatial distribution of its parameters along the legs. In contrast, we assume the system to have a perfect $\mathbb{Z}_2$ symmetry to interchange between the legs, and investigate the effects of spatial randomness which preserves this symmetry in the strong-disorder limit. To this end, we apply a strong randomness real-space renormalization group technique and explore the resulting phase diagram. We identify three disorder-dominated phases, including an intermediate phase between a disordered superconductor and a disordered insulator. The latter insulating phase can be mapped to a XY spin-chain in a spin glass phase, while the intermediate phase turns out to be a Bose glass.