Scale invariant solids

TL;DR

This paper explores scale invariance in solid materials, modeling both manifest and spontaneously broken cases using AdS/CFT and EFT, and discusses implications for elastic responses and sound speeds.

Contribution

It introduces a new class of EFTs for solids with scale invariance, including a family that generalizes the conformal solid and allows small sound speeds.

Findings

Modeling of elastic response with realistic sound speeds

Introduction of a new one-parameter family of EFTs

Discussion of Lorentz invariance effects on sound speeds

Abstract

Scale invariance (SI) can in principle be realized in the elastic response of solid materials. There are two basic options: that SI is a manifest symmetry or that it is spontaneously broken. The manifest case corresponds physically to the existence of a non-trivial infrared fixed point with phonons among its degrees of freedom. We use simple bottom-up AdS/CFT constructions to model this case. We characterize the types of possible elastic response and discuss how the sound speeds can be realistic, that is, sufficiently small compared to the speed of light. We also study the spontaneously broken case using Effective Field Theory (EFT) methods. We present a new one-parameter family of nontrivial EFTs that includes the previously known `conformal solid' as a particular case as well as others which display small sound speeds. We also point out that an emergent Lorentz invariance at low energies could affect by order-one factors the relation between sound speeds and elastic moduli.