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Holographic Aspects of Fermi Liquids in a Background Magnetic Field

Tameem Albash, Clifford V. Johnson

TL;DR

The paper demonstrates that in holographic Fermi liquids dual to dyonic AdS$_4$ black holes at $T=0$, an external magnetic field ${\cal H}$ induces a finite set of quasiparticle levels with a dispersion that evolves from non-Landau toward Landau-like as ${\cal H}$ grows. Using a probe Dirac fermion, it systematically derives boundary Green's functions and analyzes the spectrum through separable and fully numerical methods, revealing a gap, a ridge, and discrete poles corresponding to a Fermi surface at finite $k_F$. A key finding is that increasing ${\cal H}$ lifts energy levels and can eliminate quasiparticles when the ridge and gap cease to cross, indicating a controlled deformed non-Landau Fermi liquid rather than a simple Landau fluid. The results highlight rich, potentially experimentally relevant strongly coupled physics accessible via holography, with the magnetic field acting as a tunable probe of the Fermi surface structure.

Abstract

We study the effects of an external magnetic field on the properties of the quasiparticle spectrum of the class of 2+1 dimensional strongly coupled theories holographically dual to charged AdS$_4$ black holes at zero temperature. We uncover several interesting features. At certain values of the magnetic field, there are multiple quasiparticle peaks representing a novel level structure of the associated Fermi surfaces. Furthermore, increasing magnetic field deforms the dispersion characteristics of the quasiparticle peaks from non-Landau toward Landau behaviour. At a certain value of the magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid, the quasiparticles and Fermi surface disappear.

Holographic Aspects of Fermi Liquids in a Background Magnetic Field

TL;DR

The paper demonstrates that in holographic Fermi liquids dual to dyonic AdS black holes at , an external magnetic field induces a finite set of quasiparticle levels with a dispersion that evolves from non-Landau toward Landau-like as grows. Using a probe Dirac fermion, it systematically derives boundary Green's functions and analyzes the spectrum through separable and fully numerical methods, revealing a gap, a ridge, and discrete poles corresponding to a Fermi surface at finite . A key finding is that increasing lifts energy levels and can eliminate quasiparticles when the ridge and gap cease to cross, indicating a controlled deformed non-Landau Fermi liquid rather than a simple Landau fluid. The results highlight rich, potentially experimentally relevant strongly coupled physics accessible via holography, with the magnetic field acting as a tunable probe of the Fermi surface structure.

Abstract

We study the effects of an external magnetic field on the properties of the quasiparticle spectrum of the class of 2+1 dimensional strongly coupled theories holographically dual to charged AdS black holes at zero temperature. We uncover several interesting features. At certain values of the magnetic field, there are multiple quasiparticle peaks representing a novel level structure of the associated Fermi surfaces. Furthermore, increasing magnetic field deforms the dispersion characteristics of the quasiparticle peaks from non-Landau toward Landau behaviour. At a certain value of the magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid, the quasiparticles and Fermi surface disappear.

Paper Structure

This paper contains 16 sections, 43 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Background
  3. The Probe Fermion
  4. Specializations
  5. Zero Temperature
  6. A Zero Temperature Ansatz
  7. Extracting the retarded Green's function
  8. The case of $\omega = 0$.
  9. Solutions
  10. A Separable Solution
  11. Infinite--sum cases: Full Numerical Method
  12. Accuracy of Numerics: Two Tests
  13. Observations
  14. A Gap, A Ridge, and Some Poles
  15. Dispersion of the Quasiparticle Peaks
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Solution for $H=0$ and $k_x = 1.2$ using Mathematica's NDSolve
  • Figure 2: Solution for $H=0$ using implicit method to solve PDE.
  • Figure 3: Scaling behavior of $\omega^*$ (location) and the height of the peak near the pole at $\omega = 0$ and $k_x \approx 0.918$.
  • Figure 9: Scaling behavior of $\omega_*$. The red dot is where the pole is located, which corresponds to where the two lines intersect.
  • Figure 10: Scaling behavior of $\omega_*$ for two poles at fixed magnetic field $H=-0.35$. The red dot is where the pole is located, which corresponds to the two lines intersect.