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.

arXiv comment10 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

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• Superconductor-Insulator Transition and Fermi-Bose Crossovers
• Dynamical response near quantum critical points
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Spectral function of the Higgs mode in 4-\varepsilon dimensions
• Quantum critical response: from conformal perturbation theory to holography
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Holographic response from higher derivatives with homogeneous disorder
• A Holographic Model for Quantum Critical Responses
• The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C${}_9$H${}_{18}$N${}_2$CuBr${}_4$
• Superuniversal transport near a $(2+1)$-dimensional quantum critical point
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• Momentum dissipation and holographic transport without self-duality
• Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model