Non-Fermi liquids from holography

TL;DR

The paper investigates non-Fermi-liquid behavior in (2+1) dimensions at finite density using holography by mapping a fermionic operator to a bulk spinor in a charged AdS$_4$ black hole background and computing its spectral function via the bulk Dirac equation. It provides strong evidence for Fermi-surface-like physics, including a sharp quasi-particle–like peak near a Fermi momentum $k_F$ with non-Landau scaling exponents ($z eq 1$, $oldsymbol{ obreak obreak obreak obreak obreak Ab} obreak obreak obreak obreak obreak α o 1$) and a discrete scale invariance regime for momenta below $k_S=rac{ obreak mu_q}{ obreak }$. Finite temperature smooths these features, while increasing probe charge $q$ alters the Fermi-surface structure and scaling, hinting at a flow toward more Landau-like behavior at large $q$. The work highlights the role of the near-horizon $AdS_2$ region in driving emergent scaling and log-periodic phenomena, offering a concrete holographic realization of a critical Fermi surface and suggesting new universality classes for non-Fermi liquids in strongly coupled systems.

Abstract

We report on a potentially new class of non-Fermi liquids in (2+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.

Figures (10)

• Figure 1: Spectral function $\textrm{Im}\, G_{22}(\omega)$ at $k=1.2 < \mu_q$ (left plot) and $k=3.0 > \mu_q$ (right plot) for $m=0$ and $q=1\; (\mu_q = \sqrt{3})$. The function asymptotes to $1$ as $|\omega| \to \infty$ as in the vacuum \ref{['vac']}. Right plot: The onset of the finite peak at $\omega \approx 1.2 \approx k - \mu_q$ roughly corresponds to the location of divergence at $\omega = k$ in the vacuum \ref{['vac']}. The function is roughly zero between $\omega \in (-k - \mu_q, k-\mu_q)$, as it is in vacuum. Left plot: The deviation from the vacuum behavior becomes significant.
• Figure 2: 3d plots of $\textrm{Im}\, G_{11}(\omega, k)$ and $\textrm{Im}\, G_{22}(\omega, k)$ for $m=0$ and $q=1 \, (\mu_q = \sqrt{3})$. In the right plot the ridge at $k \gg \mu_q$ corresponds to the smoothed-out peaks at finite density of the divergence at $\omega = k$ in the vacuum. As one decreases $k$ to a value $k_F \approx 0.92 < \mu_q$, the ridge in $\textrm{Im}\, G_{22}$ develops into an (infinitely) sharp peak indicative of a Fermi surface.
• Figure 3: $\textrm{Re}\, G_{22}(\omega)$ (blue) and $\textrm{Im}\, G_{22}(\omega)$ (orange) at $k=0.90 < k_F$. In $\textrm{Im}\, G_{22}$, at $\omega<0$ there is a quasi-particle-like peak; for $\omega>0$, there is a much smaller 'bump'. As $k$ approaches $k_F$, the peak and the bump approach $\omega =0$ and their heights approach infinity. The dashed lines are the real and imaginary parts of the fit function \ref{['rro1']}. Although the real part slightly deviates from the fit, there is a qualitative match.
• Figure 4: Left: Plots of $\textrm{Im}\, G_{11} (k)$ (dashed line) and $\textrm{Im}\, G_{22} (k)$ as a function of $k$ at $\omega = -0.001$ ($m=0$ and $q=1$). A sharp peak in $\textrm{Im}\, G_{22} (k)$ is clearly visible near $k_F \approx 0.9185$. The height of the peak is finite. In the limit $\omega \to 0_-$, the height of the peak goes to infinity and the location of the peak approaches $k_F$ from left. Right: Plots of $\textrm{Im}\, G_{11} (k)$ (dashed line) and $\textrm{Im}\, G_{22} (k)$ as a function of $k$ at $\omega =0$. For $\omega=0$, both functions become identically zero in the region $k > {\mu_q \over \sqrt 6} = {1 \over \sqrt{2}}$. Since $k_F > 1/\sqrt{2}$, at $\omega =0$, $\textrm{Im}\, G_{22}$ is identically zero around $k_F$.
• Figure 5: $\textrm{Re}\, G_{22}(\omega)$ (blue) and $\textrm{Im}\, G_{22}(\omega)$ (orange) at $k =0.925 > k_F$. One finds a "bump" at $\omega> 0$ and a much smaller "bump" at $\omega < 0$. As $k_\perp$ approaches $0_+$, both bumps approach $\omega =0$ and their heights approach infinity. The dashed lines are the real and imaginary parts of the fit function \ref{['Bee']}. The fit is not so good for $\omega < 0$, though the qualitative trend matches.