Inability of linear axion holographic Gubser-Rocha model to capture all the transport anomalies of strange metals

Abstract

In the last decade, motivated by the concept of Planckian relaxation and the possible existence of a quantum critical point in cuprate materials, holographic techniques have been extensively used to tackle the problem of strange metals and high-$T_c$ superconductors. Among the various setups, the linear axion Gubser-Rocha model has often been considered as a promising holographic model for strange metals since endowed with the famous linear in $T$ resistivity property. As fiercely advocated by Phil Anderson, beyond $T$-linear resistivity, there are several additional anomalies unique to the strange metal phase, as for example a Fermi liquid like Hall angle -- the famous problem of the two relaxation scales. In this short note, we show that the linear axion holographic Gubser-Rocha model, which presents a single momentum relaxation time, fails in this respect and therefore is not able to capture the transport phenomenology of strange metals. We prove our statement by means of a direct numerical computation, a previously demonstrated scaling analysis and also a hydrodynamic argument. Finally, we conclude with an optimistic discussion on the possible improvements and generalizations which could lead to a holographic model for strange metals in all their glory.