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 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.

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• Impurities in superconductors
• Quantum phase transitions
• Superconductivity
• Superconductor-insulator transition
• Disordered systems
• Granular chains
• Superconducting devices
• Renormalization group