Inability of linear axion holographic Gubser-Rocha model to capture all the transport anomalies of strange metals
Yongjun Ahn, Matteo Baggioli, Hyun-Sik Jeong, Keunyoung Kim
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 it is endowed with the famous linear in $T$ resistivity property. As fiercely advocated by Anderson, beyond $T$-linear resistivity, there are several additional anomalies unique to the strange metal phase, for example, a Fermi-liquid-like Hall angle---the famous problem of two relaxation scales. In this paper, 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 of the possible improvements and generalizations which could lead to a holographic model for strange metals in all their glory.