Black rubber and the non-linear elastic response of scale invariant solids

Abstract

We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

Holographic axion model: A simple gravitational tool for quantum matter

“…At low temperature, the stress-strain curve directly interpolates from the linear regime to the ν S 2 scaling. A similar power law behaviour appears in the bulk stress-strain curve [51], where there is a universal scaling…”

“…as expected for a relativistic solid system. The field theory allows for a much simpler description of the non-linear extension of elasticity theory [49,51], which will be described in the next sections. Moreover, it provides a fundamental step forward in distinguishing solids and fluids from the point of view of symmetries.…”

Dynamic properties of two-dimensional latticed holographic system

“…Gauge/gravity duality has been proved powerful tools to study strongly correlated systems and dynamical properties [2][3][4][5][6]. Anisotropy is also ubiquitous in holographic systems, such as systems with lattices, anisotropic axions, massive gravity, and so on [7][8][9][10][11][12][13]. All these models realize the anisotropy by explicitly breaking the isotropic symmetry.…”

Shear flows in far-from-equilibrium strongly coupled fluids

“…Finally, let us emphasize that one could equivalently introduce a non-trivial strain into the dual field theory using the profile of the scalars ψ I . In particular, a shear strain could be simply obtained by allowing for a background of the type ψ 1 ∼ y as done in [77,84,85]. For practical reasons, we found more convenient to introduce the strain via a metric deformation.…”