Further Evidence for Lattice-Induced Scaling

TL;DR

This work provides further evidence for a lattice-induced intermediate scaling regime in holographic transport. By extending the analysis to AdS$_4$ and AdS$_5$ backgrounds and to an ionic lattice, the authors show a robust power-law behavior in the optical conductivity, with exponents $\gamma=2/3$ in AdS$_4$ and $\gamma \approx \sqrt{3}/2$ in AdS$_5$, occurring in a common mid-infrared window $2<\omega\tau<8$ and largely independent of lattice details. The thermoelectric conductivity exhibits a matching scaling with exponent $\eta\approx5/6$, while the ionic lattice confirms the universality of the phenomenon beyond scalar lattices. Resonances tied to quasinormal modes are identified as a generic feature of holographic lattices and are separable from the scaling behavior. Overall, the results strengthen the connection between holographic lattice models and the mid-infrared transport observed in cuprates, highlighting a potentially universal, lattice-driven mechanism for anomalous scaling in strongly coupled systems.

Abstract

We continue our study of holographic transport in the presence of a background lattice. We recently found evidence that the presence of a lattice induces a new intermediate scaling regime in asymptotically $AdS_4$ spacetimes. This manifests itself in the optical conductivity which exhibits a robust power-law dependence on frequency, $σ\sim ω^{-2/3}$, in a "mid-infrared" regime, a result which is in striking agreement with experiments on the cuprates. Here we provide further evidence for the existence of this intermediate scaling regime. We demonstrate similar scaling in the thermoelectric conductivity, find analogous scalings in asymptotically $AdS_5$ spacetimes, and show that we get the same results with an ionic lattice.

Figures (12)

• Figure 1: A log-log plot of the optical conductivity for a $2+1$ dimensional system as a function of frequency. On the left, the plot has $T/\mu = .115$ and shows three different wavenumbers: squares denote $k_0 = 1$, circles denote $k_0 = 2$, and diamonds denote $k_0 = 3$. The plot on the right has $k_0 = 2$ and shows three different temperatures: the diamonds have $T/\mu = .098$, the circles have $T/\mu = .115$ and the squares have $T/\mu = .13$. In both plots, $\mu = 1.4$ and $A_0/k_0 = 3/4$.
• Figure 2: The real and imaginary parts of the thermoelectric conductivity for small frequencies. The lines are a fit to the Drude form. This is for $k_0 = 1, A_0 = .75,\mu = 1.4, T/\mu = .115$.
• Figure 3: The magnitude and phase of the thermoelectric conductivity in the intermediate scaling regime. The curve on the left is a fit to the power-law (\ref{['newscaling']}) which determines $\eta \approx 5/6$. Like the previous figure, this is for $k_0 = 1, A_0 = .75,\mu = 1.4, T/\mu = .115$.
• Figure 4: The optical conductivity both with the lattice (solid line and data points) and without (dashed line) for the $3+1$ dimensional conductor with $T/\mu= .21$ and $\mu = 1$. The lattice has $A_0 = 1.5$ and $k_0 = 2$.
• Figure 5: The optical conductivity for a $3+1$ dimensional system as a function of frequency at three different wavenumbers: squares denote $k_0 = 1$, circles denote $k_0 = 2$, and diamonds denote $k_0 = 3$. The temperature is $T/\mu = .21$, amplitude is $A_0/k_0 = 3/4$, and chemical potential is $\mu = 1$. On the left is a log-log plot of the magnitude of the conductivity, and on the right is the phase.