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 $z\ge 1$. However, for $z\ge 2(1+|\theta |/d)$, 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.

• Received 22 July 2013

DOI:https://doi.org/10.1103/PhysRevD.88.046010