Abstract:
We present a general hydrodynamic theory of transport in the vicinity of
superfluid-insulator transitions in two spatial dimensions described by
``Lorentz''-invariant quantum critical points. We allow for a weak
impurity scattering rate, a magnetic field
B
, and a deviation in the
density, $\rho$, from that of the insulator. We show that the
frequency-dependent thermal and electric linear response functions,
including the Nernst coefficient, are fully determined by a single
transport coefficient (a universal electrical conductivity), the impurity
scattering rate, and a few thermodynamic state variables. With reasonable
estimates for the parameters, our results predict a magnetic field and
temperature dependence of the Nernst signal which resembles measurements
in the cuprates, including the overall magnitude. Our theory predicts a
``hydrodynamic cyclotron mode'' which could be observable in ultrapure
samples. We also present exact results for the zero frequency transport
co-efficients of a supersymmetric conformal field theory (CFT), which is
solvable by the AdS/CFT correspondence. This correspondence maps the
$\rho$ and
B
perturbations of the 2+1 dimensional CFT to electric and
magnetic charges of a black hole in the 3+1 dimensional anti-de Sitter
space. These exact results are found to be in full agreement with the
general predictions of our hydrodynamic analysis in the appropriate
limiting regime. The mapping of the hydrodynamic and AdS/CFT results under
particle-vortex duality is also described.