Frustrated Polyelectrolyte Bundles and T=0 Josephson-Junction Arrays

We establish a one-to-one mapping between a model for hexagonal polyelectrolyte bundles and a model for two-dimensional, frustrated Josephson-junction arrays. We find that the T=0 insulator-to-superconductor transition of the quantum system corresponds to a continuous liquid-to-solid transition of the condensed charge in the finite-temperature classical system. We find that the role of the vector potential in the quantum system is played by elastic strain in the classical system. Exploiting this correspondence we show that the transition is accompanied by a spontaneous breaking of a discrete symmetry associated with the chiral patterning of the array and that at the transition the polyelectrolyte bundle adopts a universal response to shear.