title: 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 quantitative measure of deviations from self-duality between charge and vortex theories. We propose the finite wave vector compressibility as an experimental measure of the vortex condensate stiffness for neutral lattice bosons.
authors.affiliation: Physics Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel.
authors.forename: Snir
authors.initials: S
authors.lastname: Gazit
authors.affiliation: Physics Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel.
authors.forename: Daniel
authors.initials: D
authors.lastname: Podolsky
authors.affiliation: Physics Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel.
authors.forename: Assa
authors.initials: A
authors.lastname: Auerbach