Electron stars for holographic metallic criticality

TL;DR

Electron stars provide a holographic framework to study metallic quantum criticality at finite density by backreacting an Einstein-Maxwell system with a charged, zero-temperature ideal fluid of fermions. The IR geometry exhibits emergent Lifshitz scaling with a tunable exponent $z$, controlled by dimensionless parameters $etâ$ and $m̂$, and the solution flows to UV AdS$_4$ with a finite-radius star where the fluid ceases to exist. The authors derive an action for the charged fluid, outline the RN-AdS matching, and compute the electrical conductivity, finding a universal low-frequency $ ext{Re}\,σ( u) o c u^2$ behavior with a delta function at zero frequency due to translation invariance, as well as a full frequency dependence obtained numerically across the star. This work provides a framework to explore non-Landau Fermi-liquid-like behavior in strongly interacting finite-density systems and motivates further study of UV/IR connections, Fermi-surface signatures, and responses to external fields.

Abstract

We refer to the ground state of a gravitating, charged ideal fluid of fermions held at a finite chemical potential as an `electron star'. In a holographic setting, electron stars are candidate gravity duals for strongly interacting finite fermion density systems. We show how electron stars develop an emergent Lifshitz scaling at low energies. This IR scaling region is a consequence of the two way interaction between emergent quantum critical bosonic modes and the finite density of fermions. By integrating from the IR region to an asymptotically AdS_4 spacetime, we compute basic properties of the electron stars, including their electrical conductivity. We emphasize the challenge of connecting UV and IR physics in strongly interacting finite density systems.

Figures (4)

• Figure 1: Dependence of the IR dynamical critical exponent on $\hat{\beta}$. From left to right, the three curves have $\hat{m} =0 , 0.55$ and $0.7$.
• Figure 2: From bottom to top, the pressure, energy and charge density distributions for an electron star with $z=2$ and $\hat{m} = 0.36$ (corresponding to $\hat{\beta} \approx 20$). The boundary of the star is $r=r_s$. Recall that the boundary of spacetime is at $r=0$ while $r \to \infty$ is the deep IR. In the IR the thermodynamic quantities tend to their constant Lifshitz values.
• Figure 3: Dimensionless ratio of the electron star mass to its charge, normalised such that the ratio is unity for an extremal black hole. The three curves correspond, from top to bottom, to masses $\hat{m} = 0.7$, $\hat{m} = 0.36$ and $\hat{m} = 0.07$.
• Figure 4: The zero temperature real and imaginary parts of the electrical conductivity as a function of frequency. From left to right in each plot: $\{z=3, \hat{m} = 0.7 \}$, $\{z=2, \hat{m} = 0.36 \}$ and $\{z=1.5,\hat{m} = 0.15\}$. The real part also contains a delta function at $\omega=0$.