Informational properties of holographic Lifshitz field theory

TL;DR

This paper investigates the behavior of holographic entanglement entropy, mutual information, and entanglement of purification in Lifshitz holographic theories, revealing universal, monotonic, and non-monotonic properties influenced by the Lifshitz dynamical critical exponent.

Contribution

It provides new insights into how informational measures behave in Lifshitz holographic theories, including the discovery of dome-shaped and trapezoid-shaped profiles in their dependence on the critical exponent.

Findings

Informational quantities generally change monotonically with the Lifshitz exponent.

Non-monotonic behaviors occur in specific parameter and temperature regimes.

Unique dome and trapezoid shapes emerge in MI and EoP profiles versus the Lifshitz exponent.

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 monotonously 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 $z$.