Criticality in Dissipative Quantum Rotor Models

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-$T_\text{c}$ 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, $\{ \theta_{\vvr,\tau} \}$ $\in [-\pi,\pi \rangle$. The dynamical critical exponent is found to be $z \approx 1$, 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 enters on equal footing, rather than having the essentially momentum-independent Marginal Fermi Liquid-like fluctuation spectrum previously reported for the same model. When the phase-variables of the model are extended to non-compact support, the picture changes. The results for this case are also discussed.