Abstract
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.
Highlights
The interplay between quantum information theory and quantum gravity has gained increasing attention during the last decade
We see that when we heat up the system, mutual information (MI) reduces
In the left-hand plot, with fixed l = 0.7 and d = 0.4, we find that when the temperature is low, MI decreases monotonically with the increase of z and vanishes when z is beyond some critical temperature, which means that a disentangling phase transition happens
Summary
The interplay between quantum information theory and quantum gravity has gained increasing attention during the last decade. The informational quantities have been explored for holographic dual field theory with Lifshitz symmetry; see Refs.[59,60,61,62,63] and references therein. Most of these studies focused only on the HEE or MI in the background with zero charge density, and there have been few investigation on the informational quantities at finite density , especially the EoP. We shall study the related information quantities in holographic Lifshitz dual field theory with finite charge density.
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