Metal-insulator transition in holography

Abstract

We exhibit an interaction-driven metal-insulator quantum phase transition in a holographic model. Use of a helical lattice enables us to break translation invariance while preserving homogeneity. The metallic phase is characterized by a sharp Drude peak and a d.c. resistivity that increases with temperature. In the insulating phase the Drude spectral weight is transferred into a `mid-infrared' peak and to energy scales of order the chemical potential. The d.c. resistivity now decreases with temperature. In the metallic phase, operators breaking translation invariance are irrelevant at low energy scales. In the insulating phase, translation symmetry breaking effects are present at low energies. We find the near horizon extremal geometry that captures the insulating physics.

Figures (5)

• Figure 1: Progressive loss of Drude coherence in the optical conductivity. From top to bottom on the left: conventional metals, bad metals and Mott insulators.
• Figure 2: Two renormalization group flow scenarios that arise in our theories, mediating quantum phase transitions between metallic and insulating phases. In the left plot, the phase transition is mediated by an unstable fixed point, which has relevant operators (that may in addition have complex scaling dimensions). In the right plot, the phase transition occurs when the metallic fixed point itself develops a relevant deformation. One of these two possibilities must occur for the metallic phase to become unstable.
• Figure 3: The left hand plot shows the free energy as a function of pitch. The solid lines are results for $T=0$, while the dashed line shows the thermodynamically preferred phase at $T/\mu = 10^{-3}$. The solid line to the left of the plot corresponds to domain walls with an insulating IR geometry, while the solid line to the right of the plot corresponds to domain walls with metallic IR geometry. There is a continuous quantum phase transition between these two phases. The right hand plot shows the entropy density as a function of the pitch, for values of the pitch close to the critical value $p_c/\mu \approx 2.1$. As the temperature is lowered, temperatures shown from top to bottom are $T/\mu = \{10^{-3},10^{-4},10^{-5}\}$, this curve develops a step function at the critical value. Both plots have $m^2 = 0$, $\kappa = 1/\sqrt{2}$ and $\lambda/\mu = 3/2$.
• Figure 4: Optical conductivity in metallic (left) and insulating (right) phases. The three temperatures shown in each plot are $T/\mu = 0.011, 0.05, 0.12$ (top to bottom in the metallic case, bottom to top in the insulating case). The metallic phase has $p/\mu = 2.5$ and the insulating phase, $p/\mu = 1/\sqrt{2}$. Both have $m^2 = 0$, $\kappa = 1/\sqrt{2}$ and $\lambda/\mu = 3/2$. The metallic phase exhibits a Drude peak while in the insulating phase low energy spectral weight is transferred into a 'mid-infrared' peak and to interband energy scales. Note the different range of the axes on the two plots.
• Figure 5: Log-log plot of the d.c. resistivity as a function of temperature. From top to bottom, the upper (blue) lines are insulating phases with $p/\mu = 1,1/\sqrt{2}$ and the lower (red) lines are metallic phases with $p/\mu = 2.2, 2.4, 2.5$. As before, $m^2 = 0$, $\kappa = 1/\sqrt{2}$ and $\lambda/\mu = 3/2$. The resistivity $\rho_0$ is an arbitrary scale.