  We investigate the behavior of the holographic entanglement entropy (HEE) in
proximity to the quantum critical points (QCPs) of the metal-insulator
transition (MIT) in the Einstein-Maxwell-dilaton-axions (EMDA) model. Since
both the metallic phase and the insulating phase are characterized by distinct
IR geometries, we used to expect that the HEE itself characterizes the QCPs.
This expectation is validated for certain cases, however, we make a noteworthy
observation: for a specific scenario where $-1<\gamma \leq -1/3$, with $\gamma$
as a coupling parameter, it is not the HEE itself but rather the second-order
derivative of HEE with respect to the lattice wave number that effectively
characterizes quantum phase transitions (QPTs). This distinction arises due to
the influence of thermal effects. These findings present novel insights into
the interplay between HEE and QPTs in the context of the MIT, and have
significant implications for studying QPTs at finite temperatures.
