Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models

Abstract We study a relation between the thermal diffusivity (D T ) and two quantum chaotic properties, Lyapunov time (τ L ) and butterfly velocity (v B ) in strongly correlated systems by using a holographic method. Recently, it was shown that Ei:=DT,i/vB,i2τLi=x,y $$ {\mathbb{E}}_i:={D}_{T,i}/\left({v}_{{}^{B,i}}^2{\tau}_L\right)\left(i=x,y\right) $$ is universal in the sense that it is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, by analyzing the anisotropic IR scaling geometry carefully, we find the concrete expressions for Ei $$ {\mathbb{E}}_i $$ in terms of the critical dynamical exponents z i in each direction, Ei=zi/2zi−1 $$ {\mathbb{E}}_i={z}_i/2\left({z}_i-1\right) $$. Furthermore, we find the lower bound of Ei $$ {\mathbb{E}}_i $$ is always 1/2, which is not affected by anisotropy, contrary to the η/s case. However, there may be an upper bound determined by given fixed anisotropy