Decoupling in the 1D frustrated quantum XY model and Josephson junction ladders: Ising critical behavior

TL;DR

This paper investigates a generalized 1D frustrated quantum XY model with unequal couplings, revealing a decoupling of excitations and a transition from XY-Ising to pure Ising critical behavior in Josephson junction ladders.

Contribution

It demonstrates that unequal inter and intra-chain couplings lead to decoupling of excitations and a shift to pure Ising critical behavior, extending understanding of quantum phase transitions in ladder systems.

Findings

Decoupling of XY and Ising-like excitations at large interchain coupling.

Transition to pure Ising critical behavior for the chirality order parameter.

Superconductor-insulator transition in the universality class of the 2D classical XY model.

Abstract

A generalization of the one-dimensional frustrated quantum XY model is considered in which the inter and intra-chain coupling constants of the two infinite 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 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 inter and intra-chain coupling constants, the 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 2D classical XY model.