Quantum oscillations and black hole ringing

TL;DR

The paper shows that one-loop bulk fermion (and boson) contributions in holographic theories at finite density produce de Haas–van Alphen oscillations in the magnetic susceptibility, even when the classical (large-N) gravity background is featureless. A novel determinant representation expresses these one-loop corrections as sums over black hole quasinormal modes, bridging Landau-level physics and holographic spectral data. For fermions, the oscillations persist at strong coupling but appear as power-law nonanalyticities controlled by a low-energy parameter ν, rather than delta-function spikes seen in weakly coupled theories; bosons exhibit complementary, though more subtle, magnetic-field dynamics with possible periodic effects from poles emerging from branch cuts. The work highlights how bulk quantum effects capture rich, nonuniversal information about the boundary theory’s excitations and Fermi-surface-like structures, offering a concrete framework to study strong-coupling quantum oscillations and related instabilities in holographic condensed matter systems.

Abstract

We show that strongly coupled field theories with holographic gravity duals at finite charge density and low temperatures can undergo de Haas - van Alphen quantum oscillations as a function of an external magnetic field. Exhibiting this effect requires computation of the one loop contribution of charged bulk fermions to the free energy. The one loop calculation is performed using a formula expressing determinants in black hole backgrounds as sums over quasinormal modes. At zero temperature, the periodic nonanalyticities in the magnetic susceptibility as a function of the inverse magnetic field depend on the low energy scaling behavior of fermionic operators in the field theory, and are found to be softer than in weakly coupled theories. We also obtain numerical and WKB results for the quasinormal modes of charged bosons in dyonic black hole backgrounds, finding evidence for nontrivial periodic behavior as a function of the magnetic field.

Figures (9)

• Figure 1: The zero temperature magnetic susceptibility for bosons as a function of the magnetic field. The expression plotted has been made dimensionless by dividing by the sample area and multiplying by the boson mass $m$.
• Figure 2: The zero temperature magnetic susceptibility to leading order at large $N$ as a function of the magnetic field. The expression plotted has been made dimensionless by dividing by the sample area and multiplying by the chemical potential $\mu$.
• Figure 3: Motion of the quasinormal frequencies closest to the real axis as $k_\perp/\mu$ is varied from $-1$ to $+1$, according to (\ref{['eq:smallw']}). The temperature is $T=0.005\mu$. The other constants are taken to have values $q=1, \gamma=\sqrt{12},\nu = 1/3,\theta=\pi/6,h=\mu^{1/3}$.
• Figure 4: Left: Contributions of the lowest few quasinormal modes to the magnetic susceptibility, according to (\ref{['eq:meisterfermions']}), as a function of $k_\perp/\mu$. The darker line is the pole nearest the real axis. Right: the total magnetic susceptibility due to the lowest fifty modes. The temperature is $T=0.005\mu$. The constants have the same values as in figure \ref{['fig:poledancing']}. The vertical axis is proportional to $\tilde{\chi}$ of (\ref{['eq:chitilde']}).
• Figure 5: The magnetic susceptibility at $T=0$ as a function of $k_\perp/\mu$. The constants have the same values as in figure \ref{['fig:poledancing']}. The vertical axis is proportional to $\tilde{\chi}$ of (\ref{['eq:chitilde']}).