Critical capacitance and charge-vortex duality near the superfluid to insulator transition

Abstract

Using a generalized reciprocity relation between charge and vortex conductivities at complex frequencies in two space dimensions, we identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We compute the ratio of boson superfluid stiffness to vortex condensate stiffness at mirror points to be 0.21(1) for the relativistic O(2) model. The product of dynamical conductivities at mirror points is used as a test of charge-vortex duality. We propose the finite wave vector compressibility as an experimental measure of the vortex condensate stiffness for neutral lattice bosons.

10 pages, 10 figures, published version, improved discussion on the charge vortex duality in the introduction, added a supplementary material section on finite size scaling analysis of the critical energy scales, added to the supplementary material a comparison with other methods for analyzing the high frequency correction to scaling