Since holography yields exact results, even in situations where perturbation theory is not applicable, it is an ideal framework for modeling strongly correlated systems. We extend previous holographic methods to take the dynamical charge response into account and use this to perform the first holographic computation of the dispersion relation for plasmons. As the dynamical charge response of strange metals can be measured using the new technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), plasmon properties are the next milestone in verifying predictions from holographic models of new states of matter.
We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the system. Introducing momentum dissipation, we then identify its additional contribution to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of translational invariance. As the strength of SSB is increased, we observe a transition between dressed zero sound, the plasmon, and the normal sound controlled by the elastic moduli and the propagation of longitudinal phonons. This crossover is characterized by the disappearance of the plasma frequency gap in the sound mode.
For strongly interacting systems holographic duality is a powerful framework for computing e.g. dispersion relations to all orders in perturbation theory. Using the standard Reissner-Nordstöm black hole as a holographic model for a (strange) metal, we obtain exotic dispersion relations for both plasmon modes and quasinormal modes for certain intermediate values of the charge of the black hole.The obtained dispersion relations show dissipative behavior which we compare to the generic expectations from the Caldeira-Leggett model for quantum dissipation. Based on these considerations, we investigate how holography can predict higher order corrections for strongly coupled physics.
We study in detail the transverse collective modes of simple holographic models in presence of electromagnetic Coulomb interactions. We render the Maxwell gauge field dynamical via mixed boundary conditions, corresponding to a double trace deformation in the boundary field theory. We consider three different situations: (i) a holographic plasma with conserved momentum, (ii) a holographic (dirty) plasma with finite momentum relaxation and (iii) a holographic viscoelastic plasma with propagating transverse phonons. We observe two interesting new features induced by the Coulomb interactions: a mode repulsion between the shear mode and the photon mode at finite momentum relaxation, and a propagation-todiffusion crossover of the transverse collective modes induced by the finite electromagnetic interactions. Finally, at large charge density, our results are in agreement with the transverse collective mode spectrum of a charged Fermi liquid for strong interaction between quasiparticles, but with an important difference: the gapped photon mode is damped even at zero momentum. This property, usually referred to as anomalous attenuation, is produced by the interaction with a quantum critical continuum of states and might be experimentally observable in strongly correlated materials close to quantum criticality, e.g. in strange metals.
In order to make progress towards more realistic models of holographic fermion physics, we use gauge/gravity duality to compute the dispersion relations for quasinormal modes and collective modes for the electron cloud background, i.e. the non-zero temperature version of the electron star. The results are compared to the corresponding results for the Schwarzschild and Reissner-Nordström black hole backgrounds, and the qualitative differences are highlighted and discussed.
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