Abstract 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<γ≤−1/3 - 1 < γ ≤ - 1 / 3 , with
γ γ 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.
We study the entanglement entropy (EE) and the R\'enyi entropy (RE) of multiple intervals in two-dimensional
TT- deformed conformal field theory (CFT) at a finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a nontrivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cutoff radius (dual to the
TT deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected (
s-channel) and connected (
t-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.
In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We discuss the properties of phases mostly from the holographic topological entanglement entropy of the system. We find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. The behaviors of entanglement entropy at large strip size suggest that the area law still holds when including dark matter sector. We also conclude that the holographic topological entanglement entropy is useful in detecting the stability of the phase transitions. Furthermore, we derive the complete diagram of the effects of coupled parameters on the critical temperature through the entanglement entropy and analytical methods.