Quantum Fluctuations in Holographic Theories with Hyperscaling Violation

TL;DR

The authors study holographic quantum critical points with hyperscaling violation, characterized by exponents $z$ and $\theta$, by analyzing the zero-temperature fluctuations of a heavy charged probe whose boundary endpoint is the string. Using the Nambu-Goto action and appropriate boundary conditions, they derive analytical two-point functions across the $(z,\theta)$ parameter space and show a crossover: for $z+2\theta/d>2$ the late-time dynamics becomes independent of the probe mass. The work also analyzes the $z=\infty$ case via extremal RN-AdS geometries, finding $\,\mathrm{Im}\,\chi(\omega)\sim 1/\omega\,$ and logarithmic growth in time, consistent with an emergent AdS$_2$ IR CFT. Their results reproduce known Lifshitz cases ($\theta=0$) and extend to Schrödinger-like hyperscaling-violating theories, revealing universal IR behavior and mass-independence in a broad regime. These findings have implications for understanding strongly coupled quantum critical points in condensed matter systems and provide exact, parameter-space-dependent expressions for probe fluctuations and response.

Abstract

In this short note we use holographic methods to study the response of quantum critical points with hyperscaling violation to a disturbance caused by a massive charged particle. We give analytical expressions for the two-point functions of the fluctuations of the massive probe as a function of arbitrary (allowed) values of the hyperscaling violation exponent θ and the dynamical exponent z. We point out the existence of markedly different behaviors of the two-point functions in the parameter space of θ and z at late times. In particular, as expected, the late-time dynamics of the probe becomes independent of its inertial mass in the range z+2θ/d>2.

Figures (1)

• Figure 1: Schematic picture of the fluctuating string dual to a charged heavy particle coupled to a quantum critical point. The string stretches in the bulk between a D-brane at $r=r_b$ and the IR region of the geometry at $r=r_\epsilon$.