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In this paper, we explore the properties of holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) in holographic Lifshitz theory. These informational quantities exhibit some universal properties of holographic dual field theory. For most configuration parameters and temperatures, these informational quantities change monotonically with the Lifshitz dynamical critical exponent z. However, we also observe some non-monotonic behaviors for these informational quantities in some specific spaces of configuration parameters and temperatures. A particularly interesting phenomenon is that a dome-shaped diagram emerges in the behavior of MI vs z, and correspondingly a trapezoid-shaped profile appears in that of EoP vs z. This means that for some specific configuration parameters and temperatures, the system measured in terms of MI and EoP is entangled only in a certain intermediate range of z.

We investigate the features of charge transport in a novel holographic quantum phase transition (QPT) model with two metallic phases: normal metallic and novel metallic. The scaling behaviors of direct current (DC) resistivity and thermal conductivity at low temperatures in both metallic phases are numerically computed. The numerical results and the analytical ones governed by the near horizon geometry agree perfectly. Then, the features of low-frequency alternating current (AC) electric conductivity are systematically investigated. A remarkable characteristic is that the normal metallic phase is a coherent system, whereas the novel metallic phase is an incoherent system with non-vanishing intrinsic conductivity. Especially, in the novel metallic phase, the incoherent behavior becomes stronger when the strength of the momentum dissipation enhances.

We study the properties of charge transport in a novel holographic QPT (quantum phase transition) model, which has two different metallic phases: the normal metallic phase and the novel metallic one. We numerically work out the scaling behaviors of DC (direct current) resistivity at low temperatures in both different metallic phases. The numerical results are solidly in agreement with the analytical ones determined by the near horizon geometry. Then, we mainly explore the properties of the low-frequency AC (alternating current) conductivity. A remarkable characteristic is that the normal metallic phase is a coherent system with vanishing intrinsic conductivity σ Q , which is independent of the strength of the momentum dissipation. This result is in contrast with the common belief that with the strength of the momentum dissipation increasing, the system changes from a coherent phase to an incoherent one. But the novel metallic phase is an incoherent system with non-vanishing σ Q . Away from the QCP (quantum critical point), σ Q increases, which indicates that the incoherent behavior becomes stronger.