Phase transitions in the one-dimensional frustrated quantum XY model and Josephson-junction ladders

TL;DR

This paper investigates phase transitions in a one-dimensional frustrated quantum XY model, realized as Josephson-junction ladders, revealing how varying coupling ratios affects the superconductor-insulator transition and its critical behavior.

Contribution

It provides a detailed analysis of the critical behavior and phase transitions in the quantum XY ladder model, connecting it to the 2D classical XY-Ising model.

Findings

System exhibits superconductor-insulator transition at zero temperature.

Transition nature depends on the ratio of interchain to intrachain couplings.

Critical behavior aligns with the 2D classical XY-Ising model.

Abstract

A one-dimensional quantum version of the frustrated XY (planar rotor) model is considered which can be physically realized as a ladder of Josephson-junctions at half a flux quantum per plaquette. This system undergoes a superconductor to insulator transition at zero temperature as a function of charging energy. 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. Depending on the ratio between the interchain and intrachain couplings the system can have single or double transitions which is consistent with the prediction that its critical behavior should be described by the two-dimensional classical XY-Ising model.