Emergent scale invariance of disordered horizons

Abstract

We construct planar black hole solutions in AdS 3 and AdS 4 in which the boundary CFT is perturbed by marginally relevant quenched disorder. We show that the entropy density of the horizon has the scaling temperature dependence s ∼ T (d−1)/z (with d = 2, 3). The dynamical critical exponent z is computed numerically and, at weak disorder, analytically. These results lend support to the claim that the perturbed CFT flows to a disordered quantum critical theory in the IR.

Entropy production, viscosity bounds and bumpy black holes

“…Interesting examples where this can happen are cases where translation invariance is broken in the far IR. In holographic models this has recently been realized in three different ways: (i) disordered fixed points in which scaling only emerges in spatially averaged quantities [26][27][28], (ii) solutions with z = ∞ scaling in which space does not scale and hence spatial inhomogeneity is compatible with scaling [29] and (iii) cases in which the bulk matter background breaks scaling but the energy momentum tensor, and hence the metric, are scale invariant, e.g. [30][31][32].…”

Dissecting holographic conductivities

“…Another question is the sensitivity of our results to the choice of momentum relaxation mechanism: would they be modified if we had instead used random-field disorder [3,4,22,[37][38][39], or homogeneous [19,40,41] or inhomogeneous lattices [20,32,42] to break translational invariance? Furthermore, if we had broken translational invariance with electrically charged, rather than neutral, operators, would this affect the nature of transport in the system?…”

Holographic charge localization at brane intersections

“…These include setups with different holographic realizations of lattices [5][6][7][8][9][10][11][12] through periodically space-dependent sources, and also setups implementing disordered sources [13][14][15][16]. Moreover, a lattice realization where PDEs are avoided, which goes under the name of Q-lattices given its resemblance to the construction of Q-balls [17], was introduced in [18] and further explored in [19,20].…”

“…Let us start by defining the radial coordinate ζ through 16) and note that the horizon (at z = 1) is located at ζ = ∞ in the new coordinate. When expressed in this coordinate, the equations of motion for the fluctuation fields a x (z, x) and a z (z, x) in the DC limit, ω → 0, respectively take the form 17) 11 Notice that one can always choose Λ(z, x) such that it vanishes at the horizon (so at is still zero there), and also satisfies ∂zΛ(0, x) = 0 (and hence az(0, x) = 0).…”

“…The interface is now introducing a sizeable region where the charge density is augmented, producing a net enhancement of the conductivity σ DC x . 16 16 In order to roughly estimate the DC conductivity σ In figure 11 we illustratively summarize the behavior of the DC conductivities in our system. As is clear from the illustration, σ DC y (x) roughly follows the charge density, which varies along x and peaks at the interface, while σ DC x is constant, its value mainly determined by the charge density away from the interface.…”