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 five-dimensional Einstein gravity coupled to a scalar field ϕ with a non-trivial potential $V\left(\varphi \right)$. The dual 4-dimensional gauge theory is not conformal and exhibits a RG flow between two different fixed points. There are three parameters including energy scale Λ, model parameter ${\varphi }_M$ and temperature T which control the behaviour of the theory. Interestingly, we have found that $E_p$ can be used as a measure to probe the non-conformal behaviour of the theory at both zero and finite temperature. Furthermore, we have found that if one consider two different mixed state characterized by distinct values of $\frac{\Lambda }{T}$, then the correlation between the subsystems of these states can be the same independent of $\frac{\Lambda }{T}$.