Holographic study of entanglement and complexity for mixed states

TL;DR

This paper holographically investigates entanglement and complexity in mixed states within hyperscaling violating geometries, revealing how parameters like $ heta$ and $z$ influence these quantum information measures in non-relativistic strongly coupled theories.

Contribution

It introduces a holographic approach to quantify entanglement of purification and complexity for mixed states in hyperscaling violating backgrounds, extending previous studies to non-relativistic systems.

Findings

Entanglement of purification depends on $z$ and $ heta$ parameters.

Mutual complexity varies with subsystem separation and configuration.

Holographic entanglement entropy exhibits relations like the Smarr relation and Fisher information metric.

Abstract

In this paper, we holographically quantify the entanglement and complexity for mixed states by following the prescription of purification. The bulk theory we consider in this work is a hyperscaling violating solution, characterized by two parameters, hyperscaling violating exponent $\theta$ and dynamical exponent $z$. This geometry is dual to a non-relativistic strongly coupled theory with hidden Fermi surfaces. We first compute the holographic analogy of entanglement of purification (EoP), denoted as the minimal area of the entanglement wedge cross section and observe the effects of $z$ and $\theta$. Then in order to probe the mixed state complexity we compute the mutual complexity for the BTZ black hole and the hyperscaling violating geometry by incorporating the holographic subregion complexity conjecture. We carry this out for two disjoint subsystems separated by a distance and also when the subsystems are adjacent with subsystems making up the full system. Furthermore, various aspects of holographic entanglement entropy such as entanglement Smarr relation, Fisher information metric and the butterfly velocity has also been discussed.