Holographic non-Fermi liquid fixed points

TL;DR

This work analyzes holographic non-Fermi liquid fixed points by focusing on finite-density fermions in a gravity dual, where the low-energy physics is controlled by an emergent IR CFT living on an AdS2 throat.A detailed gravity calculation shows how the IR correlator G_k(ω) ∝ ω^{2ν_k} feeds into the full retarded Green's function via matched asymptotic expansions between UV and IR regions, yielding Fermi-surface structures with non-Fermi-liquid dispersion, vanishing residue, and varied quasiparticle lifetimes.The study connects UV data (the presence and location of a Fermi surface) to IR geometry, discusses finite-temperature effects that replace branch cuts with poles, and explores implications for transport and potential superconducting instabilities within holographic setups.Overall, the paper provides a concrete, calculable framework to understand NFL-like metallic states in strongly coupled systems using AdS/CFT, highlighting how IR fixed-point dynamics can produce a sharp Fermi surface without long-lived quasiparticles.

Abstract

Techniques arising from string theory can be used to study assemblies of strongly-interacting fermions. Via this `holographic duality', various strongly-coupled many body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared fixed point theory which is represented by an AdS_2 region in the dual gravitational description. Here we describe in detail the gravity calculation of this IR correlation function. This article is a contribution to a special issue of Phil. Trans. A on the normal state of the cuprates; as such, we also provide some review and context.

Figures (9)

• Figure 1: The left figure indicates a series of block spin transformations labelled by a parameter $r$. The right figure is a cartoon of AdS space, which organizes the field theory information in the same way. In this sense, the bulk picture is a hologram: excitations with different wavelengths get put in different places in the bulk image.
• Figure 2: A comparison of the geometries associated with a CFT (left), and with a system with a mass gap (right).
• Figure 3: 3d plots of ${\rm Im } G_{1}(\omega, k)$ and ${\rm Im } G_{2}(\omega, k)$ 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 develops into an (infinitely) sharp peak indicative of a Fermi surface.
• Figure 4: The geometry of the extremal $AdS_{d+1}$ charged black hole.
• Figure 5: Shown here is a sequence of Schrödinger potentials for the scalar wave equation in the RN black hole. The horizontal axis is a 'tortoise' coordinate $s$ which makes the wave equation into a one dimensional Schrödinger problem. The role of the energy in the Schrödinger problem is played by $-k^2$. The red dotted curve is a cartoon of the boundstate wavefunction at $\omega=0$ with energy $-k_F^2$; the blue curve which becomes horizontal at large negative $s$ (the IR region) is the associated Schrödinger potential for $\omega=0$. As $\omega$ increases from zero, the potential develops a well in the IR region (the other blue curves), into which the boundstate can tunnel. The width of the barrier is $\Delta s \sim -2\ln|\omega|$, and the height is $\nu_{k_F}^2$; hence the tunneling amplitude which determines the decay rate of the Fermi surface boundstate is $e^{ - \text{area}} \sim \omega^{2 \nu_{k_F} }$.