Pinning of holographic sliding stripes

In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data of the dual background black hole solution. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent z > 2. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids. arXiv:1904.11445v3 [hep-th] 30 Sep 2019where the vevs A, B = (δρ, δs, π , λ , π ⊥ , λ ⊥ ) and the corresponding sources are

Section: Discussionmentioning

confidence: 99%

Diffusion and universal relaxation of holographic phonons

Amoretti

Areán

Goutéraux

et al. 2019

“…As a consequence, it is important to investigate such interplay within scenarios at strong coupling lacking a quasiparticle description, for example within holography. The coexistence of SSB and EXB has already been introduced in several holographic models [21,32,34,35]. In this manuscript we analyze the nature of this phenomenon in detail both from the point of view of the spectra of modes and from the optical transport features.…”

Section: Pseudo-spontaneous Breaking Of Translations and Pseudo-phononsmentioning

confidence: 96%

“…See[32,34,35,[53][54][55][56][57][58] for other studies of the interplay of spontaneous and explicit breaking of translations in holography and field theory.…”

mentioning

confidence: 99%

A unified description of translational symmetry breaking in holography

Ammon

Baggioli

Alba

2019

131

We provide a complete and unified description of translational symmetry breaking in a simple holographic model. In particular, we focus on the distinction and the interplay between explicit and spontaneous breaking. We consider a class of holographic massive gravity models which allow to range continuously from one situation to the other. We study the collective degrees of freedom, the electric AC conductivity and the shear correlator in function of the explicit and spontaneous scales. We show the possibility of having a sound-to-diffusion crossover for the transverse phonons. Within our model, we verify the validity of the Gell-Mann-Oakes-Renner relation. Despite of strong evidence for the absence of any standard dislocation induced phase relaxation mechanism, we identify a novel relaxation scale controlled by the ratio between the explicit and spontaneous breaking scales. Finally, in the pseudospontaneous limit, we prove analytically the relation, which has been discussed in the literature, between this novel relaxation scale, the mass of the pseudo-phonons and the Goldstone diffusivity. Our numerical data confirms this analytic result.

“…Simpler homogeneous models were investigated in [37][38][39][40]. This opened the way to extensive studies of the effective low energy dynamics of holographic density waves, pinned or not, [1,19,24,25,[41][42][43][44][45][46][47]. The effective, hydrodynamic theory of pinned charge density waves of [22,23] provides in most cases the correct framework to interpret these results.…”

Section: Introductionmentioning

confidence: 99%

Gapless and gapped holographic phonons

Amoretti

Areán

Goutéraux

et al. 2020

We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in [1] continues to hold in this model for weak enough explicit breaking.1 These holographic homogeneous models inspired analogous constructions [20] which account for the translation-breaking dynamics in a purely field-theoretical context. For a generalization of such constructions to inhomogeneous case see [21]. 2 The pinning frequency can also be written more intuitively as ω o = c ⊥ k o with k o ≡ m the inverse length scale defined by the phonon mass and c ⊥ ≡ G/χ P P the shear sound velocity. 10 Based on private communication with the authors of [46] and [48].