Friedel oscillations and horizon charge in 1D holographic liquids

TL;DR

This paper demonstrates the presence of Friedel oscillations in a 1D holographic system with a charged horizon, linking magnetic monopoles to Fermi surface features and confirming Luttinger's theorem.

Contribution

It reveals how magnetic monopoles in a 3D gravity dual cause Friedel oscillations and relate to the charge behind the horizon, providing insights into holographic Fermi surfaces.

Findings

Friedel oscillations occur at a wavevector counting horizon charge

Magnetic monopoles induce these oscillations in the correlation functions

Fermi momentum matches Luttinger's theorem when monopoles saturate Dirac quantization

Abstract

In many-body fermionic systems at finite density correlation functions of the density operator exhibit Friedel oscillations at a wavevector that is twice the Fermi momentum. We demonstrate the existence of such Friedel oscillations in a 3d gravity dual to a compressible finite-density state in a (1+1) dimensional field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and all the charge is behind a bulk horizon. The bulk gauge theory is compact and so there exist magnetic monopole tunneling events. We compute the effect of these monopoles on holographic density-density correlation functions and demonstrate that they cause Friedel oscillations at a wavevector that directly counts the charge behind the bulk horizon. If the magnetic monopoles are taken to saturate the bulk Dirac quantization condition then the observed Fermi momentum exactly agrees with that predicted by Luttinger's theorem, suggesting some Fermi surface structure associated with the charged horizon. The mechanism is generic and will apply to any charged horizon in three dimensions. Along the way we clarify some aspects of the holographic interpretation of Maxwell electromagnetism in three bulk dimensions and show that perturbations about the charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.