Zero sound in strange metals with hyperscaling violation from holography

TL;DR

This paper investigates how hyperscaling violation affects the zero sound mode in holographic strange metals, revealing conditions under which zero sound exists and characterizing the resulting quantum liquids.

Contribution

It extends holographic models of strange metals by analyzing the impact of hyperscaling violation on zero sound and identifies new regimes of quantum liquid behavior.

Findings

Zero sound exists for $z < 2(1+| heta|/d)$ with hyperscaling violation.

No well-defined zero sound quasiparticle for $z geq 2(1+| heta|/d)$.

Systems behave as Fermi or Bose liquids under specific hyperscaling conditions.

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 $\theta$). 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 $z < 2(1+|\theta|/d)$, where the positivity of the specific heat and the null energy condition of the background dictate that $\theta<0$ and $z\geq 1$. However, for $z \geq 2(1+|\theta|/d)$, there is no well-defined quasiparticle for the zero sound. The systems behave like Fermi liquid for $2|\theta|=dz$ and like Bose liquid for $2|\theta| = qdz$ (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.