Mixed state entanglement in deformed field theory at finite temperature

TL;DR

This paper investigates how mixed state entanglement measures, specifically entanglement of purification and negativity, behave in a finite temperature deformed field theory using holographic duality, revealing that deformation reduces entanglement.

Contribution

It introduces the computation of entanglement wedge cross section and holographic negativity in a $Tar{T}$ deformed finite temperature field theory with a finite cutoff, analyzing their behavior across different regimes.

Findings

Deformation decreases entanglement between subsystems.

Temperature and deformation have similar effects on entanglement measures.

Entanglement measures decline with increasing deformation.

Abstract

We study mixed state entanglement measures in a higher dimensional $T\bar{T}$ deformed field theory at finite temperature. The holographic dual is described by AdS$_{d+1}$ black brane geometry with a finite cutoff. We compute the entanglement wedge cross section (EWCS), proposed to be dual to entanglement of purification (EoP) and holographic entanglement negativity (HEN) for strip like subsystems. The behavior of EWCS and HEN is studied across different regimes of temperature and deformation parameter. It is observed that the deformation and temperature exhibit similar effects on these two entanglement measures. Increasing the deformation leads to a decrease in the entanglement between the subsystems.