The quasi-normal modes of quantum criticality
arXiv:1210.4166 · doi:10.1103/PhysRevB.86.235115
Abstract
We study charge transport of quantum critical points described by conformal field theories in 2+1 spacetime dimensions. The transport is described by an effective field theory on an asymptotically anti-de Sitter spacetime, expanded to fourth order in spatial and temporal gradients. The presence of a horizon at non-zero temperatures implies that this theory has quasi-normal modes with complex frequencies. The quasi-normal modes determine the poles and zeros of the conductivity in the complex frequency plane, and so fully determine its behavior on the real frequency axis, at frequencies both smaller and larger than the absolute temperature. We describe the role of particle-vortex or S-duality on the conductivity, specifically how it maps poles to zeros and vice versa. These analyses motivate two sum rules obeyed by the quantum critical conductivity: the holographic computations are the first to satisfy both sum rules, while earlier Boltzmann-theory computations satisfy only one of them. Finally, we compare our results with the analytic structure of the O(N) model in the large-N limit, and other CFTs.
29+14 pages, 10+2 figures. v4: minor corrections and additions
References in corpus (17)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
- The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
- Quantum critical transport in clean graphene
- Quantum critical transport, duality, and M-theory
- A Sharp Peak of the Zero-Temperature Penetration Depth at Optimal Composition in BaFe2(As1-xPx)2
- Sum Rules for the Optical and Hall Conductivity in Graphene
- Theory of a continuous Mott transition in two dimensions
- Ohm's Law at strong coupling: S duality and the cyclotron resonance
- Quantum-critical relativistic magnetotransport in graphene
- SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
- Destruction of Neel order in the cuprates by electron-doping
- Sum Rules from an Extra Dimension
- Compressible quantum phases from conformal field theories in 2+1 dimensions
- Magnetothermoelectric Response near Quantum Critical Points
- Current fluctuations near to the 2D superconductor-insulator quantum critical point
- Signatures of the nematic ordering transitions in the thermal conductivity of d-wave superconductors