Finite-size-scaling analyses of the chiral order in the Josephson-junctionladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consi der an extreme quantum limit where each superconductor grain (order paramet er) is represented by S = 1/2 spin. So far, the semi-classical S -> infinit y case, where each spin reduces to a plane rotator: has been considered ext ensively. We found that in the case of S = 1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except i n a region, where attractive intrachain and, to our surprise, repulsive int erchain interactions both exist. On the contrary, for considerably wide ran ge of parameters, the superconductor (XY) order is kept critical. The prese nt results are regarded as a demonstration of the critical phase accompanyi ng chiral-symmetry breaking predicted for frustrated XXZ chain field-theore tically.