Logarithmic two-Point Correlation Functions from a z = 2 Lifshitz Model

The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It is found that the retarded correlators are stable in the sense that all quasinormal modes are situated in the lower half-plane of complex frequencies. Correlators in the longitudinal channel exhibit features that are reminiscent of a structure usually obtained in field theories that are logarithmic, i.e. contain an indecomposable highest weight representation. This suggests the model at hand as a candidate for a gravity dual of a logarithmic field theory with anisotropic scaling symmetry.Comment: 31 pages, 2 figure

Analogue Gravity Models From Conformal Rescaling

Analogue gravity is based on a mathematical identity between quantum field theory in curved space-time and the propagation of perturbations in certain condensed matter systems. But not every curved space-time can be simulated in such a way, because one does not only need a condensed matter system that generates the desired metric tensor, but that system then also has to obey its own equations of motion. And specifying the metric tensor that one wishes to realize usually overdetermines the underlying condensed matter system, such that its equations of motion are in general not fulfilled, in which case the desired metric does not have an analogue. Here, we show that the class of metrics that have an analogue is bigger than what a first cursory consideration might suggest. This is due to the analogue metric only being defined up to a choice of parametrization of the perturbation in the underlying condensed matter system. In this way, the class of analogue gravity models can be vastly expanded. In particular, we demonstrate how this freedom of choice can be used to insert an intermediary conformal factor. Then, as a corollary, we find that any metric conformal to a Painlev\'e--Gullstrand type line element can, potentially, result as an analogue of a perturbation propagating in a non-viscous, barotropic fluid.Comment: 12 page

Holographic Response of Electron Clouds

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-Nordstr\"om black hole backgrounds, and the qualitative differences are highlighted and discussed.Comment: 27 page

Holographic Plasmons

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.Comment: 12 pages, 2 figures. v2: Minor changes v3: Minor adjustments v4: Published versio

Holographic Plasmon Relaxation with and without Broken Translations

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. Upon dialing the strength of the SSB, we observe an increase of the longitudinal sound speed controlled by the elastic moduli and a decrease in the plasma frequency of the gapped plasmon. We comment on the condensed matter interpretation of this mechanism.Comment: v2: improved discussions, added results in the SSB section, references added; matching the published version in JHE

Exotic Holographic Dispersion

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-Nordst\"om 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.Comment: 12 pages, 14 figure

Plasmons in holographic graphene

We demonstrate how self-sourced collective modes - of which the plasmon is a prominent example due to its relevance in modern technological applications - are identified in strongly correlated systems described by holographic Maxwell theories. The characteristic omega proportional to root k plasmon dispersion for 2D materials, such as graphene, naturally emerges from this formalism. We also demonstrate this by constructing the first holographic model containing this feature. This provides new insight into modeling such systems from a holographic point of view, bottom-up and top-down alike. Beyond that, this method provides a general framework to compute the dynamical charge response of strange metals, which has recently become experimentally accessible due to the novel technique of momentum-resolved electron energy-loss spectroscopy (M-EELS). This framework therefore opens up the exciting possibility of testing holographic models for strange metals against actual experimental data.Peer reviewe

Analog models for holographic transport

The gauge-gravity duality and analog gravity both relate a condensed matter system to a gravitational theory. This makes it possible to use gravity as an intermediary to establish a relation between two different condensed matter systems: the strongly coupled system from the gauge-gravity duality and the weakly coupled gravitational analog. We here offer some examples for relations between observables in the two different condensed matter systems. In particular, we show how the equations characterizing Green functions and fast order transport coefficients in holographic models can be mapped to those describing phenomena in an analog gravitational system, which allows, in principle, to obtain the former by measuring the latter.Peer reviewe