Universal scaling properties of extremal cohesive holographic phases

TL;DR

The work presents a universal framework for classifying cohesive holographic IR phases at finite density via four exponents $z$, $\theta$, $\xi$, and $\zeta$, yielding two main classes depending on the IR relevance of the current. It demonstrates this parameterization across three model families—Massive vectors, Electron stars, and Phases with Chern-Simons couplings—and derives the scaling of observables including thermodynamics, low-frequency AC conductivity, and the spectrum of electric fluctuations, while linking nonlocal probes to the bulk electric flux through the Hartnoll-Radicevic observable and a deformed entanglement entropy $S_E^\lambda$. The conduction exponent $\zeta$ is shown to universally control the IR optical conductivity, and the cohesion exponent $\xi$ governs when the deformed entropy deviates from the Ryu-Takayanagi prescription. The results offer a robust, model-independent map from bulk IR data to boundary observables and propose new nonlocal diagnostics for cohesion vs fractionalization in strongly coupled quantum critical phases.

Abstract

We show that strongly-coupled, translation-invariant holographic IR phases at finite density can be classified according to the scaling behaviour of the metric, the electric potential and the electric flux introducing four critical exponents, independently of the details of the setup. Solutions fall into two classes, depending on whether they break relativistic symmetry or not. The critical exponents determine key properties of these phases, like thermodynamic stability, the (ir)relevant deformations around them, the low-frequency scaling of the optical conductivity and the nature of the spectrum for electric perturbations. We also study the scaling behaviour of the electric flux through bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and characterize the deviation from the Ryu-Takayanagi prescription in terms of the critical exponents.

Figures (2)

• Figure 1: Behaviour of the Schrödinger potential in the IR in $d=2$ (Left pannel: $z\neq1$; right pannel: $z=1$). In the red region, it diverges to $-\infty$, the optical conductivity vanishes at low frequency and the spectrum is gapless. In the blue region, it diverges to $+\infty$, linear response theory breaks down and the spectrum will be gapped if the potential also diverges in the UV.
• Figure 2: Typical behaviour of the function $D(\rho)$ depending on the sign of $\xi$ and the relative signs of $\lambda\sigma_0$ and the integration constant $C$. The horizontal lines represent different values of $1/4G_N$, and solutions of $D(\rho_0)=1/4G_N$ are highlighted in red and with a thicker line. The solutions can either reach the boundary with or without a disconnected piece in the bulk (a bubble), or there might be no solution, or just a bubble in the bulk which does not reach the boundary (though see main text).