Zero sound in strange metals with hyperscaling violation from holography

Parijat Dey; Shibaji Roy

doi:10.1103/PhysRevD.88.046010

paper

Zero sound in strange metals with hyperscaling violation from holography

arXiv:1307.0195 · doi:10.1103/PhysRevD.88.046010

Abstract

Hyperscaling violating `strange metal' phase of heavy fermion compounds can be described holographically by probe D-branes in the background of a Lifshitz space-time (dynamical exponent $z$ and spatial dimensions $d$ ) with hyperscaling violation (corresponding exponent $θ$ ). Without the hyperscaling violation, strange metals are known to exhibit zero sound mode for $z < 2$ analogous to the Fermi liquids. In this paper, we study its fate in the presence of hyperscaling violation and find that in this case the zero sound mode exists for $z < 2 (1 + ∣ θ ∣/ d)$ , where the positivity of the specific heat and the null energy condition of the background dictate that $θ < 0$ and $z \geq 1$ . However, for $z \geq 2 (1 + ∣ θ ∣/ d)$ , there is no well-defined quasiparticle for the zero sound. The systems behave like Fermi liquid for $2∣ θ ∣ = d z$ and like Bose liquid for $2∣ θ ∣ = q d z$ (where $q$ is the number of spatial dimensions along which D-branes are extended in the background space), but in general they behave as a new kind of quantum liquid. We also compute the AC conductivity of the systems and briefly comment on the results.

16 pages, no figures; v2: minor changes, references added; v3: eq.(43) and the related text have been corrected, more refs added, version to appear in Phys. Rev. D

Zero sound in strange metals with hyperscaling violation from holography

Abstract

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