Abstract
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.
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