Semi-Holographic Fermi Liquids

TL;DR

The paper develops a semi-holographic framework in which a dynamical boundary fermion couples to a strongly interacting CFT with a gravity dual, capturing universal IR features of holographic non-Fermi liquids. By deriving the coupled χ–Ψ system, it shows how the IR sector, often described by an AdS$_2$ fixed point, governs non-Fermi-liquid behavior and how the model can be generalized to AdS$_4$ and Lifshitz geometries, including lattice and impurity effects. It analyzes a broad set of relevant operators—fermionic bilinears, density multilinears, and spin-orbit couplings—studying their impact on stability, fixed points, and potential phase transitions, including the possibility of alternate quantization near the Fermi surface. The work also discusses UV–IR matching: mapping UV AdS$_4$ data to IR AdS$_2$ physics, and demonstrates how double-trace deformations can tune or even erase the Fermi surface, highlighting a tunable, doping-like control of low-energy metallic states in a controlled holographic setting.

Abstract

We show that the universal physics of recent holographic non-Fermi liquid models is captured by a semi-holographic description, in which a dynamical boundary field is coupled to a strongly coupled conformal sector having a gravity dual. This allows various generalizations, such as a dynamical exponent and lattice and impurity effects. We examine possible relevant deformations, including multi-trace terms and spin-orbit effects. We discuss the matching onto the UV theory of the earlier work, and an alternate description in which the boundary field is integrated out.

Figures (4)

• Figure 1: Fermi momentum as a function of radius, shown in the WKB approximation. a) The minimal ingredients to give rise to non-Fermi liquid behavior, a domain wall Fermi sea plus $AdS_2$ horizon. b) Over most of the parameter space of Ref. Faulkner:2009wj there is also a Fermi liquid in the IR bulk (entire shaded region). Backreaction converts the geometry to Lifshitz form HPST, whose Fermi sea is shown in dark shading.
• Figure 2: a) The geometric sum leading to the fermion correlator (\ref{['gcorr']}). The solid line represents $G_0$ and the dashed line represents ${\cal G}_0$. b) The geometric sum (\ref{['gof']}), where an $\times$ represents the double-trace perturbation.
• Figure 3: Left: flows represented by the $AdS_4$ RN geometry in the presence of a probe fermion when $\Delta_{\vec{k}} < 1$. The vertical direction is an energy scale and $\Lambda_k > \Lambda_k'$ for the two different flows. The standard (alternative) quantized theory is denoted $AdS_2^0$ ($AdS_2^\infty$). Right: the fermi surface with $\Delta_{\vec{k}} < 1$ is a quantum critical point in $k$ space, with $AdS_2^\infty$ controlling the physics.
• Figure 4: Size of the fermi surfaces $k_\star^{\alpha=2}$ (solid) and $k_\star^{\alpha=1}$ (dashed) as a function of the relevant double-trace coupling $\texttt{x}$ in units of $\mu$ for three choices of $q$ and $\Delta_4 = 5/4$. The splitting due to spin orbit coupling increases with $q$, and is absent here for $q=0$. Note that the IR scaling dimension $\Delta_{\vec{k}_\star}$ increases with "doping" because it increases with $k_\star$.