Holographic study of shear viscosity and butterfly velocity for magnetic field-driven quantum criticality

Abstract

We investigate the shear viscosity and butterfly velocity of a magnetic field-induced quantum phase transition in five dimensional Einstein-Maxwell-Chern-Simons theory, which is holographically dual to a class of strongly coupled quantum field theories with chiral anomalies. Our analysis reveals that the ratio of longitudinal shear viscosity to entropy density η_∥/s exhibits a pronounced non-monotonic dependence on temperature T when the magnetic field B is slightly below the critical value B_c of the quantum phase transition. In particular, it can develop a distinct minimum at an intermediate temperature. This contrasts sharply with the monotonic temperature scaling observed at and above B_c, where η_∥/s follows the scaling T^2/3 at B = B_c and transitions to T ² for B > B_c as T → 0. The non-vanishing of η_∥/s for B < B_c in the zero temperature limit suggests that it could serve as a good order parameter of the quantum phase transition. We also find that all butterfly velocities change dramatically near the quantum phase transition, and thus their derivatives with respect to B can be independently used to detect the quantum critical point.