Holographic zero sound at finite temperature

TL;DR

This work uses gauge-gravity duality to analyze finite-temperature, finite-density collective modes in a strongly coupled gauge theory with fundamental matter, realized by the D3/D7 probe-brane setup. By examining density–density correlators and their quasinormal-mode poles, the authors identify three regimes—collisionless quantum, collisionless thermal, and hydrodynamic—whose boundaries are set by scales $T/\mu$ and $(T/\mu)^2$ and that exhibit a collision-induced crossover from propagating zero-sound to diffusion. Remarkably, the holographic zero sound persists at small $T$ with a dispersion reminiscent of Landau zero sound, even though the underlying thermodynamics are atypical ($c_V\propto T^6/d$) and a conventional Fermi surface is not evident. The findings demonstrate that Landau-like collective modes can arise in strongly coupled holographic systems, offering insights into non-Fermi-liquid quantum liquids and guiding future extensions to other finite-density holographic frameworks.

Abstract

We use gauge-gravity duality to study the temperature dependence of the zero sound mode and the fundamental matter diffusion mode in the strongly coupled {\cal N}=4 SU(N_c) supersymmetric Yang-Mills theory with N_f {\cal N}=2 hypermultiplets in the N_c>>1, N_c>>N_f limit, which is holographically realized via the D3/D7 brane system. In the high density limit μ>>T, three regimes can be identified in the behavior of these modes, analogous to the collisionless quantum, collisionless thermal and hydrodynamic regimes of a Landau Fermi-liquid. The transitions between the three regimes are characterized by the parameters T/μand (T/μ)^2 respectively, and in each of these regimes the modes have a distinctively different temperature and momentum dependence. The collisionless-hydrodynamic transition occurs when the zero sound poles of the density-density correlator in the complex frequency plane collide on the imaginary axis to produce a hydrodynamic diffusion pole. We observe that the properties characteristic of a Landau Fermi-liquid zero sound mode are present in the D3/D7 system despite the atypical T^6/μ^3 temperature scaling of the specific heat and an apparent lack of a directly identifiable Fermi surface.

Figures (13)

• Figure 1: Relative scales in the hydrodynamic, collisionless thermal and collisionless quantum regimes of a Landau Fermi-liquid.
• Figure 2: A sketch of the dependence of the sound mode damping on frequency in the hydrodynamic (I), collisionless thermal (II) and collisionless quantum (III) regimes of a Landau Fermi-liquid. First sound propagates in region I while the zero sound mode exists in regions II and III.
• Figure 3: The temperature dependence of the sound attenuation coefficient $\Gamma_q$ in various regimes of a Landau Fermi-liquid. Above: A sketch of the dependence in the hydrodynamic (I), collisionless thermal (II) and collisionless quantum (III) regimes. Below: Temperature dependence of the acoustic attenuation in liquid $\,^3$He at P=32 kPa measured at both 15.4 MHz ($\bigcirc$) and 45.5 MHz ($\Box$). The lines through the data correspond to $\log \Gamma_q \sim 2 \log T$ and $\log \Gamma_q \sim - 2 \log T$ in the collisionless thermal and hydrodynamic regimes, respectively, in agreement with Table \ref{['tab1']}. Reprinted with permission from Abel et al.Abel:1966zz. Copyright (1966) by the American Physical Society.
• Figure 4: The holographic zero sound peak in the collisionless quantum regime. The longitudinal spectral function is shown at $\bar{m}=0$, $\tilde{d}=10^6$, $\bar{q}=0.4$.
• Figure 5: The dispersion relation of the dominant pole at $\bar{m}=0$, $\tilde{d}=10^6$. Dots show numerical results at low $T$ and the solid lines are the analytic result (\ref{['eq:zerosound']}) at $T=0$.