Quantum criticality in dissipative quantum two-dimensional XY and Ashkin-Teller models: Application to the cuprates

In a recent paper [V. Aji and C. M. Varma, Phys. Rev. Lett. 99, 067003 (2007)] we have shown that the dissipation driven quantum phase transition of the two-dimensional XY model represents a universality class where the correlations at criticality are 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.