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We investigate the behavior of the holographic entanglement entropy (HEE) inproximity to the quantum critical points (QCPs) of the metal-insulatortransition (MIT) in the Einstein-Maxwell-dilaton-axions (EMDA) model. Sinceboth the metallic phase and the insulating phase are characterized by distinctIR geometries, we used to expect that the HEE itself characterizes the QCPs.This expectation is validated for certain cases, however, we make a noteworthyobservation: 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-orderderivative of HEE with respect to the lattice wave number that effectivelycharacterizes quantum phase transitions (QPTs). This distinction arises due tothe influence of thermal effects. These findings present novel insights intothe interplay between HEE and QPTs in the context of the MIT, and havesignificant implications for studying QPTs at finite temperatures.

Diagnosing quantum phase transition via holographic entanglement entropy at finite temperature