Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence
Sean A. Hartnoll, Diego M. Hofman
TL;DR
The paper addresses how quantum oscillations in magnetic susceptibility behave in strongly interacting quantum critical non-Fermi liquids. It employs holographic duality to perform a nonperturbative calculation of the oscillatory response in a 2+1D theory, yielding a general expression for $\Omega_{\text{osc}}$ and the resulting $\chi_{\text{osc}}$ that is controlled by a critical exponent $\nu$. A key finding is a generalized Lifshitz-Kosevich scaling: for $\nu<\tfrac{1}{2}$ the oscillation amplitude decays as $\chi_{\text{osc}} \sim e^{- T^{2\nu}}$, while at the marginal value $\nu = \tfrac{1}{2}$ the textbook LK form is recovered; the work provides a practical formalism to compute oscillation amplitudes in general holographic fermionic theories. The results offer a concrete template for interpreting experiments in strongly correlated materials and point to extensions to include disorder and alternative holographic geometries.
Abstract
We characterize quantum oscillations in the magnetic susceptibility of a quantum critical non-Fermi liquid. The computation is performed in a strongly interacting regime using the nonperturbative holographic correspondence. The temperature dependence of the amplitude of the oscillations is shown to depend on a critical exponent nu. For general nu the temperature scaling is distinct from the textbook Lifshitz-Kosevich formula. At the `marginal' value nu = 1/2, the Lifshitz-Kosevich formula is recovered despite strong interactions. As a by-product of our analysis we present a formalism for computing the amplitude of quantum oscillations for general fermionic theories very efficiently.