A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball

Abstract

Using the AdS/CFT correspondence, we calculate a fermionic spectral function in a 2+1 dimensional non-relativistic quantum field theory which is dual to a gravitational theory in the $AdS_4$ background with a charged black hole. The spectral function shows no quasiparticle peak but the Fermi surface is still well defined. Interestingly, all momentum points inside the Fermi surface are critical and the gapless modes are defined in a {\it critical Fermi ball} in the momentum space.

Figures (4)

• Figure 1: The contour plot of the zero temperature spectral function as a function of energy and momentum for $q = -\sqrt{3}$ and $\alpha = 10$. The darkest region represents the area with no spectral weight and the brightest region, the highest value of the spectral function.
• Figure 2: The energy distribution curves of the spectral function for $q = -\sqrt{3}$ and $\alpha = 10$ at momenta (a) $k=3$, (b) $k=5$, (c) $k=7$, (d) $k=9$, (e) $k=11$ and (f) $k=13$.
• Figure 3: The spectral function at $k=3$ as a function of imaginary frequency with the same parameters used in Fig. \ref{['fig:Ak']}.
• Figure 4: Temperature dependence of the spectral function at $k=6$. With a fixed $\alpha=10$, $q$ is changed to tune temperature to $T=0$ (solid line), $T=\frac{1}{4 \pi}$ (dashed line) and $T=\frac{10}{4 \pi}$ (dotted line).