Inhomogeneity simplified

TL;DR

This paper introduces novel inhomogeneous matter field models with square root Lagrangians that maintain isotropic, homogeneous black brane metrics, providing insights into conductivity behaviors relevant to heavy fermion systems.

Contribution

It presents new models involving square root terms related to massive gravity and brane limits, deriving analytical and numerical results for conductivity in these systems.

Findings

DC resistivity exhibits linear growth with temperature.

Optical conductivity shows minima at finite frequencies.

Models replicate key features of heavy fermion systems.

Abstract

We study models of translational symmetry breaking in which inhomogeneous matter field profiles can be engineered in such a way that black brane metrics remain isotropic and homogeneous. We explore novel Lagrangians involving square root terms and show how these are related to massive gravity models and to tensionless limits of branes. Analytic expressions for the DC conductivity and for the low frequency scaling of the optical conductivity in phenomenological models are derived, and the optical conductivity is studied in detail numerically. The square root Lagrangians are associated with linear growth in the DC resistivity with temperature and also lead to minima in the optical conductivity at finite frequency, suggesting that our models may capture many features of heavy fermion systems.