Holographic Spectral Functions with Momentum Relaxation

TL;DR

This paper investigates how momentum relaxation affects fermionic spectral functions in two holographic models, revealing similar phase diagrams despite different geometries and contrasting effects on DC conductivities.

Contribution

It constructs comprehensive phase diagrams of spectral functions in models with momentum relaxation, highlighting similarities and differences in spectral and transport properties.

Findings

Spectral function phase diagrams are similar across models.

Momentum relaxation impacts spectral phases similarly in both models.

Effects on DC conductivities differ significantly between models.

Abstract

We study (fermionic) spectral functions in two holographic models, the Gubser-Rocha-linear axion model and the linear axion model, where translational symmetry is broken by axion fields linear to the boundary coordinates ($\psi_{I}=\beta \delta_{Ii} x^{i}$). Here, $\beta$ corresponds to the strength of momentum relaxation. The spectral function is computed by the fermionic Green's function of the bulk Dirac equation, where a fermion mass, $m$, and a dipole coupling, $p$, are introduced as input parameters. By classifying the shape of spectral functions, we construct complete phase diagrams in ($m,p,\beta$) space for both models. We find that two phase diagrams are similar even though their background geometries are different. We also find that the effect of momentum relaxation on the (spectral function) phases of two models are similar even though the effect of momentum relaxation on the DC conductivities of two models are very different. We suspect that this is because holographic fermion does not back-react to geometry in our framework.