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Quantum criticality and black holes

Subir Sachdev, Markus Mueller

TL;DR

The paper surveys how quantum critical transport in 2+1 dimensions—where quasiparticles are ill-defined—can be understood using the AdS/CFT correspondence, which maps a strongly coupled CFT3 to gravity in AdS4. It emphasizes universal transport bounds and coefficients, such as $\tau \ge \frac{\hbar}{k_B T}\Phi_\tau$ and $\sigma = \frac{e^{*2}}{h}\Phi_\sigma$, and shows how black hole physics yields exact results for these quantities, including $\eta/s$ and $s$, in the quantum critical regime. It then connects these holographic results to experimental contexts: the superfluid–insulator transition and graphene, predicting a hydrodynamic cyclotron resonance and novel thermo-electric responses. The work also outlines how dyonic black holes and Einstein–Maxwell dynamics underpin these predictions, and surveys further directions for holographic approaches to condensed matter, including nonrelativistic and parity-violating quantum critical points. Overall, the paper demonstrates a unifying framework where black hole physics informs the transport of strongly correlated quantum critical systems.

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.

Quantum criticality and black holes

TL;DR

The paper surveys how quantum critical transport in 2+1 dimensions—where quasiparticles are ill-defined—can be understood using the AdS/CFT correspondence, which maps a strongly coupled CFT3 to gravity in AdS4. It emphasizes universal transport bounds and coefficients, such as and , and shows how black hole physics yields exact results for these quantities, including and , in the quantum critical regime. It then connects these holographic results to experimental contexts: the superfluid–insulator transition and graphene, predicting a hydrodynamic cyclotron resonance and novel thermo-electric responses. The work also outlines how dyonic black holes and Einstein–Maxwell dynamics underpin these predictions, and surveys further directions for holographic approaches to condensed matter, including nonrelativistic and parity-violating quantum critical points. Overall, the paper demonstrates a unifying framework where black hole physics informs the transport of strongly correlated quantum critical systems.

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.

Paper Structure

This paper contains 5 sections, 19 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quantum critical transport
  3. Black holes and the AdS/CFT correspondence
  4. The superfluid-insulator transition and graphene
  5. Recent developments

Figures (2)

  • Figure 1: The connections between quantum criticality and black holes described in this paper
  • Figure 2: Phase diagram of the Bose Hubbard model at integer filling. Dashed lines are crossovers, while the full line is the Kosterlitz-Thouless transition at $T_{KT}$.