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

TL;DR

This paper explores the charge-vortex duality near the superfluid-insulator transition, identifying capacitance as a measure of vortex condensate stiffness and proposing experimental measures for it.

Contribution

It introduces a generalized reciprocity relation for conductivities, computes the ratio of superfluid to vortex stiffness, and suggests experimental methods to measure vortex condensate stiffness.

Findings

Ratio of superfluid to vortex stiffness is approximately 0.21.

Product of dynamical conductivities at mirror points confirms charge-vortex duality.

Finite wave vector compressibility proposed as an experimental measure.

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.