Effective Holographic Theories for low-temperature condensed matter systems

Abstract

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents $(\gamma ,\delta )$ that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the $(\gamma ,\delta )$ plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when $\gamma =\delta$ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole $(\gamma ,\delta )$ plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

(v3): Added discussion on the UV completion of the solutions, and on extremal spectra in the charged case. Expanded discusion on insulating extremal solutions. Many other refinements and corrections. 126 pages. 48 figures

References in corpus (10)

• Building an AdS/CFT superconductor
• Holography from Conformal Field Theory
• Exploring improved holographic theories for QCD: Part II
• Metallic AdS/CFT
• Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics
• Chiral symmetry breaking as open string tachyon condensation
• Deconfinement and Gluon Plasma Dynamics in Improved Holographic QCD
• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Shear Modes, Criticality and Extremal Black Holes
• On Holographic Superconductors with DC Current

Cited by in corpus (10)

• A holographic critical point
• Fermi surfaces and gauge-gravity duality
• Domain Wall Holography for Finite Temperature Scaling Solutions
• Holography of charged dilatonic black branes at finite temperature
• The particle number in Galilean holography
• Holographic quantum criticality from multi-trace deformations
• Conductivity in the anisotropic background
• Charged Dilatonic Black Holes and their Transport Properties
• Strange Metallic Behaviour and the Thermodynamics of Charged Dilatonic Black Holes
• Gravity/Spin-model correspondence and holographic superfluids