Quantum criticality in a dissipative (2+1)-dimensionalXYmodel of circulating currents in high-Tccuprates

Abstract

We present large-scale Monte Carlo results for the dynamical critical exponent $z$ and the spatio-temporal two-point correlation function of a (2+1)-dimensional quantum $XY$ model with bond dissipation, proposed to describe a quantum critical point in high-${T}_{c}$ cuprates near optimal doping. The phase variables of the model, originating with a parametrization of circulating currents within the CuO${}_{2}$ unit cells in cuprates, are compact, ${{\ensuremath{\theta}}_{\mathbf{r},\ensuremath{\tau}}}\ensuremath{\in}[\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi}\ensuremath{\rangle}$. The dynamical critical exponent is found to be $z\ensuremath{\approx}1$, and the spatio-temporal correlation functions are explicitly demonstrated to be isotropic in space-imaginary time. The model thus has a fluctuation spectrum where momentum and frequency enter on equal footing, rather than having the essentially momentum-independent marginal Fermi-liquid-like fluctuation spectrum previously reported for the same model.