Quantum criticality and black holes

Abstract

Many condensed matter experiments explore the finite temperature dynamics of systemsnear quantum critical points. Often, there are no well-defined quasiparticle excitations, andso quantum kinetic equations do not describe the transport properties completely. Thetheory shows that the transport coefficients are not proportional to a mean free scatteringtime (as is the case in the Boltzmann theory of quasiparticles), but are completelydetermined by the absolute temperature and by equilibrium thermodynamic observables.Recently, explicit solutions of this quantum critical dynamics have become possible via theanti-de Sitter/conformal field theory duality discovered in string theory. This shows thatthe quantum critical theory provides a holographic description of the quantumtheory of black holes in a negatively curved anti-de Sitter space, and relates itstransport coefficients to properties of the Hawking radiation from the black hole. Wereview how insights from this connection have led to new results for experimentalsystems: (i) the vicinity of the superfluid–insulator transition in the presence ofan applied magnetic field, and its possible application to measurements of theNernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Diracelectrons in graphene and the prediction of a hydrodynamic cyclotron resonance.