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Novel metals and insulators from holography

Aristomenis Donos, Jerome P. Gauntlett

TL;DR

This paper builds simple holographic models with a Q-lattice in $D=4$ gravity to realize $d=3$ CFTs at finite density, producing zero-temperature ground states that break translation in one or more directions and exhibit either insulating or metallic behavior. By analyzing anisotropic and isotropic sectors, it identifies power-law low-frequency optical conductivities whose exponents are fixed by the IR fixed points and derives an elegant horizon-data formula for the DC conductivity at finite temperature. The authors construct UV-complete black holes that interpolate between $AdS_4$ in the UV and IR fixed points, classifying the IR behavior across three ranges of the parameter $\\\gamma$ and demonstrating metal-insulator transitions driven by lattice strength. A general method for computing $\\sigma_{DC}$ from horizon data is provided, enabling analytic scaling relations and cross-checks with optical conductivities, thereby advancing holographic realizations of incoherent metals and insulators with broken translational symmetry.

Abstract

Using simple holographic models in $D=4$ spacetime dimensions we construct black hole solutions dual to $d=3$ CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions with broken translation invariance, either in one or both spatial directions, which exhibit insulating or metallic behaviour depending on the parameters of the holographic theory. For low temperatures and small frequencies, the real part of the optical conductivity has a power-law behaviour, with the exponent determined by the ground state. We also obtain an expression for the the DC conductivity at finite temperature in terms of horizon data of the black hole solutions.

Novel metals and insulators from holography

TL;DR

This paper builds simple holographic models with a Q-lattice in gravity to realize CFTs at finite density, producing zero-temperature ground states that break translation in one or more directions and exhibit either insulating or metallic behavior. By analyzing anisotropic and isotropic sectors, it identifies power-law low-frequency optical conductivities whose exponents are fixed by the IR fixed points and derives an elegant horizon-data formula for the DC conductivity at finite temperature. The authors construct UV-complete black holes that interpolate between in the UV and IR fixed points, classifying the IR behavior across three ranges of the parameter and demonstrating metal-insulator transitions driven by lattice strength. A general method for computing from horizon data is provided, enabling analytic scaling relations and cross-checks with optical conductivities, thereby advancing holographic realizations of incoherent metals and insulators with broken translational symmetry.

Abstract

Using simple holographic models in spacetime dimensions we construct black hole solutions dual to CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions with broken translation invariance, either in one or both spatial directions, which exhibit insulating or metallic behaviour depending on the parameters of the holographic theory. For low temperatures and small frequencies, the real part of the optical conductivity has a power-law behaviour, with the exponent determined by the ground state. We also obtain an expression for the the DC conductivity at finite temperature in terms of horizon data of the black hole solutions.

Paper Structure

This paper contains 14 sections, 58 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Anisotropic ground states which break translation invariance in one spatial direction
  3. Mode analysis
  4. Conductivity
  5. Scaling and finite temperature
  6. Black holes in a UV completion
  7. Q-lattice black holes
  8. $-1<\gamma\le -1/3$
  9. $-1/3<\gamma\le -1/12$
  10. $-1/12<\gamma$
  11. Isotropic ground states with no spatial translational symmetry
  12. Calculating the DC conductivity
  13. Examples
  14. Non-translationally invariant $\eta$-geometries

Figures (1)

  • Figure 1: The blue curves indicate the low-temperature behaviour of the entropy for the Q-lattice black holes which approach, in the IR and at $T=0$, the new fixed point solutions of section \ref{['sec2']}. The red-dashed line indicate the scaling behaviour expected from \ref{['enscal']}. Panel (a) is for $\gamma=-2/3$, $k/\mu=\sqrt{2}/20$ and $\lambda/\mu=3/2$, with $s\sim T^{0.014}$. The green curve in this panel shows another black hole solution for $\gamma=-2/3$, $k/\mu=\sqrt{2}/20$, but with a smaller lattice deformation of $\lambda/\mu=1/10$, which approaches a translationally invariant $AdS_2\times\mathbb{R}^2$ solution with non-zero entropy density. Panel (b) is for $\gamma=-1/6$, $k/\mu=\sqrt{2}/20$ and $\lambda/\mu=1/10$ with $s\sim T^{0.080}$. Panel (c) is for $\gamma=0$, $k/\mu=\sqrt{2}/20$ and $\lambda/\mu=1$ with $s\sim T^{0.11}$. Panel (d) is for $\gamma=9/2$, $k/\mu=\sqrt{2}/20$, $\lambda/\mu=1$ with $s\sim T^{0.79}$.