Entanglement of Purification as a Measure of Non-Conformality

TL;DR

This paper investigates the entanglement of purification in a non-conformal holographic model, demonstrating its effectiveness as a measure of non-conformal behavior at various temperatures and revealing invariance in subsystem correlations across different states.

Contribution

It introduces the use of entanglement of purification as a probe for non-conformality in holographic models with scalar fields and explores its behavior at different energy scales and temperatures.

Findings

$E_p$ effectively probes non-conformal behavior.

Correlation between subsystems can be invariant across different states.

$E_p$ varies with energy scale and temperature in predictable ways.

Abstract

We have studied the entanglement of purification $E_p$ in a non-conformal holographic model which is a 5- dimensional Einstein gravity coupled to a scalar field $\phi$ with a non-trivial potential $V(\phi)$. The dual 4-dimensional gauge theory is not conformal and exhibits a FG flow between two different fixed points. There are three parameters including energy scale $\Lambda$, model parameter $\phi_M$ and temperature $T$ which control the behavior of the model. Interestingly, we have found that $E_p$ can be used as a measure to probe the non-conformal behavior of the theory at both zero and finite temperature. Furthermore, we have found that if one considers two different mixed states characterized by distinct values of $\frac{\Lambda}{T}$, then the correlation between the subsystems of these states can be the same independent of $\frac{\Lambda}{T}$.