Dynamics Near Quantum Criticality in Two Space Dimensions

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Focusing on the dynamical aspects of quantum criticality in two dimensions, this work explores two energy scales: the Higgs mode and dual vortex superfluid stiffness. It reveals how the amplitude mode can be observed near criticality through scalar susceptibility and optical conductivity. The author applies charge-vortex duality to investigate the capacitance of a Mott insulator during the superfluid-insulator phase transition. Detailed numerical methods, including a worm algorithm for O(N) models, enhance the findings, which are significant for current experiments in cold atomic systems and disordered superconductors.