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

A bstract 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.