Probing the charge-vortex duality near the superfluid-to-insulator transition

We study the charge vortex duality near the superfluid-to-insulator quantum phase transition in d=2+1 dimensions. We use a generalized reciprocity relation between charge and vortex conductivities at complex frequencies to identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We then compute the ratio of boson superfluid stiffness to vortex condensate stiffness at mirror points to be 0.21(1). This corroborates and provides a quantitative measure to the non self-dual nature of the charge-vortex duality. We further study deviations from self-duality at finite frequency by computing the product of Matsubara frequency conductivities at mirror points across the phase transition. Finally, we propose experimental realizations that test our predictions in THz spectroscopy of disordered superconductors and cold atomic systems trapped in an optical lattice. [1] S. Gazit, D. Podolsky, A. Auerbach, arXiv:1407.1055 (2014)