Collective Excitations of Holographic Quantum Liquids in a Magnetic Field

TL;DR

This paper uses holography to analyze collective excitations in strongly coupled quantum liquids under magnetic fields, revealing a transition from hydrodynamic diffusion to zero sound modes with a magnetic field-dependent gap.

Contribution

It provides a detailed holographic study of the crossover between hydrodynamic and collisionless regimes in quantum liquids with magnetic fields, highlighting the magnetic field's effect on collective modes.

Findings

Hydrodynamic charge diffusion dominates at low frequencies.

Zero sound mode appears at high frequencies with a B-dependent gap.

Crossover frequency is approximately independent of B.

Abstract

We use holography to study N=4 supersymmetric SU(Nc) Yang-Mills theory in the large-Nc and large-coupling limits coupled to a number Nf << Nc of (n+1)-dimensional massless supersymmetric hypermultiplets in the Nc representation of SU(Nc), with n=2,3. We introduce a temperature T, a baryon number chemical potential mu, and a baryon number magnetic field B, and work in a regime with mu >> T,\sqrt{B}. We study the collective excitations of these holographic quantum liquids by computing the poles in the retarded Green's function of the baryon number charge density operator and the associated peaks in the spectral function. We focus on the evolution of the collective excitations as we increase the frequency relative to T, i.e. the hydrodynamic/collisionless crossover. We find that for all B, at low frequencies the tallest peak in the spectral function is associated with hydrodynamic charge diffusion. At high frequencies the tallest peak is associated with a sound mode similar to the zero sound mode in the collisionless regime of a Landau Fermi liquid. The sound mode has a gap proportional to B, and as a result for intermediate frequencies and for B sufficiently large compared to T the spectral function is strongly suppressed. We find that the hydrodynamic/collisionless crossover occurs at a frequency that is approximately B-independent.