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Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity

Norihiro Iizuka, Nilay Kundu, Prithvi Narayan, Sandip P. Trivedi

TL;DR

This work analyzes fermionic two-point functions in 2+1d strongly coupled systems via a holographic dual with dilaton gravity and a U(1) gauge field. By parameterizing the near-horizon geometry with β and γ, it identifies regimes where boundary fermions behave as a Fermi liquid or a non-Fermi liquid, and it reveals a continuous transition controlled by β+γ, including special cases with vanishing entropy. The study links the existence and width of quasi-particles to the near-horizon IR data, showing that even without thermodynamic phase changes, the fermionic spectrum can undergo dramatic qualitative changes. It also discusses the role of finite temperature in taming singularities and outlines the limitations of the large-N, two-derivative gravity framework, along with directions for string-theory embeddings and future extensions.

Abstract

We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasi-particles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.

Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity

TL;DR

This work analyzes fermionic two-point functions in 2+1d strongly coupled systems via a holographic dual with dilaton gravity and a U(1) gauge field. By parameterizing the near-horizon geometry with β and γ, it identifies regimes where boundary fermions behave as a Fermi liquid or a non-Fermi liquid, and it reveals a continuous transition controlled by β+γ, including special cases with vanishing entropy. The study links the existence and width of quasi-particles to the near-horizon IR data, showing that even without thermodynamic phase changes, the fermionic spectrum can undergo dramatic qualitative changes. It also discusses the role of finite temperature in taming singularities and outlines the limitations of the large-N, two-derivative gravity framework, along with directions for string-theory embeddings and future extensions.

Abstract

We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasi-particles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.

Paper Structure

This paper contains 31 sections, 195 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Dilaton Gravity System
  3. The Solutions
  4. More on the Solutions
  5. Thermodynamics of the Slightly Non-Extremal Black Brane
  6. Taming the Singularity
  7. Conductivity
  8. Fermionic Two Point Function
  9. $\beta+\gamma>1$
  10. Some General Comments for the Cases $\beta+\gamma\le 1$
  11. More on the $\beta+\gamma=1$ case
  12. Case $\beta + \gamma <$1
  13. The Transition from $\beta+\gamma=1$ to $\beta+\gamma<1$
  14. Conclusions
  15. Results
  16. ...and 16 more sections

Figures (5)

  • Figure 1: Region Allowed by the Constraints
  • Figure 2: Region with $\beta+\gamma>1$ in Blue; $\beta+\gamma<1$ in Green.
  • Figure 3: Region in $\alpha,\delta$ plane satisfying $\nu_1 < -4 \delta k$.
  • Figure 4: Numerical solution interpolating between the near horizon solution and $AdS_4$ for $\alpha=1$, $\delta=0.6$ and $d_1 =0.01$. The second plot shows that $a'(r)$ and $b'(r)$ approach $1$. Red lines denote $a$, Blue lines denote $b$.
  • Figure 5: Numerical solution for $\phi$, for $\alpha=1$, $\delta=0.6$.