Finite-size-scaling analyses of the chiral order in the Josephson-junction ladder 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 consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S = 1/2 spin. So far, the semi-classical S -> infinity case, where each spin reduces to a plane rotator: has been considered extensively. We found that in the case of S = 1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically.