Abstract
We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry-they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory. Massive gravity theories thus emerge as versatile and convenient theories to model generic types of translational symmetry breaking: explicit, spontaneous, and a mixture of both. The nature of the breaking is encoded in the radial dependence of the graviton mass. As an application of the model, we compute the temperature dependence of the shear modulus and find that it features a glasslike melting transition.
Highlights
Crete Center for Theoretical Physics, Institute for Theoretical and Computational Physics Department of Physics, University of Crete, 71003 Heraklion, Greece
We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry—they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory
With the present Letter we shall rectify this deficiency by presenting a class of simple holographic models featuring transverse phonons and elastic properties
Summary
Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy. We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry—they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory. Despite the various directions and applications pursued, a fundamental piece of the condensed matter phenomenology is still missing in the holographic puzzle: a concrete, simple, and clear realization of phonons with standard properties as dictated by elasticity theory; see e.g. Ref. [13], where gapped transverse phonons were identified, with the size of the gap being directly related to the asymptotic behavior of the graviton mass. This suggests a clear way to realize gapless phonons by ensuring a rapid enough decay of mgðuÞ towards the boundary. Previous works with partial success in this direction are listed in Ref. [15]
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