
Abstract: The Hallmark of quantum critical phenomena is the emergence of universal energy scales near the quantum phase transition. I will present work studying the critical excitation spectrum of the two dimensional superfluid to insulator transition.
In particular, I will show that, in the superfluid phase, the amplitude (Higgs) mode survives, as a well-defined resonance, arbitrarily close to the critical point.
In addition, I will demonstrate that the critical capacitance serves as a measure to the elusive dual vortex superfluid stiffness in the Mott phase. The predictions are pertinent to recent experiments in cold atomic systems and disordered superconductors.