Holographic entanglement negativity and thermodynamics in backreacted AdS black hole

Abstract

We investigate holographic entanglement negativity (HEN) as a probe of mixed state quantum correlations in a deformed AdS black hole background with backreaction sourced by a string cloud. The bulk geometry is dual to a strongly coupled large-$N_c$ gauge theory at finite temperature, backreacted by a finite density of heavy static fundamental quarks. Alongside holographic entanglement entropy (HEE), we analyze entanglement thermodynamics and establish a first law like relation in the small backreaction regime by identifying the deformed black hole at zero temperature as the natural ground state of the dual field theory. Using analytic expansions in the low and high temperature limits, we compute the HEN for adjacent, disjoint and bipartite subsystem configurations and examine its dependence on the backreaction parameter $ρ$. Our results reveal a clear regime dependence: at low temperature, backreaction suppresses the negativity, signaling a reduction of distillable quantum correlations while at high temperature the negativity is enhanced due to the monotonic $ρ$-dependence of near horizon contributions. We further compare the behavior of HEN with HEE and mutual information, demonstrating that entanglement negativity provides a sharper diagnostic of the competition between thermal and quantum correlations in holographic plasmas with matter backreaction.