A Simple Holographic Insulator

TL;DR

This work presents a simple, nonsingular holographic insulator built from a domain-wall RG flow between two AdS_4 vacua, driven by a relevant double-trace deformation and a ψ-dependent gauge kinetic function. Both the low-temperature DC conductivity and the zero-temperature optical conductivity vanish as a power of temperature and frequency, with the common exponent equal to the IR scaling dimension Δ_ψ of the scalar operator, illustrating a clean IR-controlled mechanism for insulating behavior. By tuning the bulk gauge-scalar coupling g across a critical value g_c, the model naturally transitions to a conductor with a Drude-like peak, offering a controlled holographic realization of an insulator–metal transition in a translation-invariant setting. The results provide a compact framework for RG flows between CFTs with explicit transport signatures and highlight the role of IR fixed-point data in determining low-energy transport properties.

Abstract

We present a simple holographic model of an insulator. Unlike most previous holographic insulators, the zero temperature infrared geometry is completely nonsingular. Both the low temperature DC conductivity and the optical conductivity at zero temperature satisfy power laws with the same exponent, given by the scaling dimension of an operator in the IR. Changing a parameter in the model converts it from an insulator to a conductor with a standard Drude peak.

Figures (6)

• Figure 1: A plot of our potential. The minimum is at $\psi_c = \sqrt{2}\ln(1+\sqrt{2})$ with minimum value $V(\psi_c) = - 8$.
• Figure 2: The value of $\langle\mathcal{O}\rangle$ vs. $T/(-\kappa)$ with critical value $T_c/(-\kappa) \approx .616$.
• Figure 3: (Left) Log-log plot of our numerical solution for $f(r)$ in the IR (blue dots). The red line (which goes through all the points) is the analytic planar AdS-Schwarzschild solution. The two curves correspond to $T/(-\kappa) = .037$ (top) and $T/(-\kappa) = 7.06 \times 10^{-3}$ (bottom). One can see the transition from the linear Schwarzschild behavior to the quadratic $AdS_4$ behavior. (Right) The scalar field on the horizon as a function of temperature. At low $T$, it scales like $T^{\Delta_\psi}$.
• Figure 4: Log-log plot of the optical conductivity vs. frequency at $T/(-\kappa) = 7.06\times 10^{-3}$. The line of best fit gives $\sigma \sim \omega^{2.75}$. Our analytic solution says that it should be a power law with an exponent $2\Delta_\psi \approx 2.744$.
• Figure 5: Fit of optical conductivity to a Drude type curve, $\sigma(\omega) = \frac{K\tau}{1-i\omega\tau}$. For this plot, we chose $g=10$ at a temperature $T/(-\kappa) = .037$, and found $K = 540$, $\tau = .485$.