  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.
