Quantum-Criticality in Dissipative Quantum Two-Dimensional XY and Ashkin-Teller Models: Application to the Cuprates

TL;DR

This paper analyzes the quantum-critical behavior of dissipative 2D XY and Ashkin-Teller models, revealing local spatial correlations and power-law temporal correlations, with implications for understanding loop order in cuprates.

Contribution

It provides a detailed analysis of the dissipation-driven quantum phase transition, highlighting the decoupling of space and time singularities and mapping the Ashkin-Teller model to the XY model at criticality.

Findings

Local criticality with space correlations decaying rapidly

Power-law correlations in time at the transition

Mapping of the Ashkin-Teller model to the XY model in the critical regime

Abstract

In a recent paper [V. Aji and C.M. Varma, Phys. Rev. Lett. {\bf 99}, 167003 (2007) \cite{aji1}] we have shown that the dissipation driven quantum phase transition of the 2D xy model represents a universality class where the correlations at criticality is local in space and power law in time. Here we provide a detailed analysis of the model. The local criticality is brought about by the decoupling of infrared singularities in space and time. The former leads to a Kosterlitz Thouless transition whereby the excitations of the transverse component of the velocity field (vortices) unbind in space. The latter on the other hand leads to a transition among excitations (warps) in the longitudinal component of the velocity field, which unbind in time. The quantum Ashkin-Teller model, with which the observed loop order in the Cuprates is described maps in the critical regime to the quantum xy model. We also discuss other models which are expected to have similar properties.