Vortex duality: watching the dual side with order propagators

Abstract

In condensed matter physics, Kramers-Wannier duality implies that the state disordered by quantum fluctuations or temperature actually corresponds with an ordered state formed from the topological excitations of the 'original' ordered state. At first sight it might appear to be impossible to observe this dual order using means associated with the original order. Although true for Ising models, we consider in this paper the well known vortex duality, in particular in the quantum interpretation in 2+1D where it is associated with the quantum phase transition from a superfluid to a Bose Mott insulator. Here, the disordered Mott insulating state is at the same time a dual superconductor corresponding with a Bose condensate of vortices. We present a simple formalism making it possible to compute the velocity propagator associated with the superfluid in terms of the degrees of freedom of the dual theory. The Mott insulator is characterized by a doublet of massive modes and we demonstrate that one of these modes is nothing else than the longitudinal photon (gauged second sound) of the dual superconductor. For increasing momenta, the system rediscovers the original order, and the effect on the velocity correlator is that the longitudinal photon looses its pole strength. The quantum critical regime as probed by the velocity correlator is most interesting. We demonstrate that at infinite wavelength the continua of critical modes associated with second sound and the dual longitudinal photon are indistinguishable. However, at finite momenta they behave differently, tracking the weight reshuffling found in the quasiparticle spectrum of the disorder state closely.

arXiv comment12 pages, 8 figures

References in corpus (14)

• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• Critical fluctuations in superconductors and the magnetic field penetration depth
• High precision Monte Carlo study of the 3D XY-universality class
• Topological phase-fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors
• Extreme Type-II Superconductors in a Magnetic Field: A Theory of Critical Fluctuations
• Duality in 2+1D Quantum Elasticity: superconductivity and Quantum Nematic Order
• Anomalous scaling dimensions and stable charged fixed-point of type-II superconductors
• Critical Behavior of the Meissner Transition in the Lattice London Superconductor
• Low-Magnetic Field Critical Behavior in Strongly Type-II Superconductors
• Hausdorff dimension of critical fluctuations in abelian gauge theories
• A new broken U(1)-symmetry in extreme type-II superconductors
• Critical exponent η_ϕof the Lattice London Superconductor and vortex loops in the 3D XY model

Cited by in corpus (9)

• Dual gauge field theory of quantum liquid crystals in two dimensions
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Observing the fluctuating stripes in high Tc superconductors
• Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions
• The emergence of gauge invariance: the stay-at-home gauge versus local-global duality
• Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D
• Type-II Bose-Mott insulators
• Critical $1$- and $2$-point spin correlations for the $O(2)$ model in $3d$ bounded domains
• Theoretical proposal for dual transformation between the Josephson effect and quantum phase slip in single junction systems and nanowires