Dynamics and conductivity near quantum criticality

Relativistic O(N) field theories are studied near the quantum-critical point in two space dimensions. We compute dynamical correlations by large-scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For N=3 and 4, we confirm its ω3 rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For N=2, the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons (Josephson arrays), the power-law rise above the Higgs mass increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be σc*=0.3(±0.1)×4e2/h and describe a generalization of the worm algorithm to N>2. We use a singular value decomposition error analysis for the numerical analytic continuation.