Quantum criticality and black holes

TL;DR

This paper explores the connection between quantum critical systems in condensed matter physics and black holes via the AdS/CFT duality, revealing how holographic models inform transport properties and experimental phenomena.

Contribution

It demonstrates how holographic duality provides new insights into quantum critical transport and predicts novel effects in condensed matter systems.

Findings

Transport coefficients depend on temperature and thermodynamics, not quasiparticle scattering.

Holographic models relate black hole properties to condensed matter transport.

Predictions include hydrodynamic cyclotron resonance in graphene.

Abstract

Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport co-efficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport co-efficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.