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 $\eta_\parallel/s$ 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 $\eta_\parallel/s$ follows the scaling $T^{2/3}$ at $B=B_c$ and transitions to $T^2$ for $B>B_c$ as $T\to0$. The non-vanishing of $\eta_\parallel/s$ 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.