Decoupling in the one-dimensional frustrated quantumXYmodel and Josephson-junction ladders: Ising critical behavior

A generalization of the one-dimensional frustrated quantum $\mathrm{XY}$ model is considered in which the interchain and intrachain coupling constants of the two infinite $\mathrm{XY}$ (planar rotor) chains have different strengths. The model can describe the superconductor to insulator transition due to charging effects in a ladder of Josephson junctions in a magnetic field with half a flux quantum per plaquette. From a fluctuation-effective action, this transition is expected to be in the universality class of the two-dimensional classical $\mathrm{XY}$-Ising model. The critical behavior is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. It is found that, unlike the previous studied case of equal interchain and intrachain coupling constants, the $\mathrm{XY}$ and Ising-like excitations of the quantum model decouple for large interchain coupling, giving rise to pure Ising model critical behavior for the chirality order parameter and a superconductor-insulator transition in the universality class of the two-dimensional classical $\mathrm{XY}$ model.