Entanglement of Purification as a Measure of Non-Conformality

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 $\varphi$ with a non-trivial potential $V(\varphi )$. 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 ${\varphi }_M$ 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 $\frac{\Lambda }{T}$.

10 pages, 11 figures