Information theoretic measures for Lifshitz system

TL;DR

This paper explores how various information theoretic measures behave in excited Lifshitz spacetimes, providing insights into entanglement properties of dual quantum field theories with Lifshitz symmetry.

Contribution

It calculates holographic mutual information, entanglement wedge cross section, negativity, and complexity for excited Lifshitz states, extending previous pure state analyses with first-order perturbations.

Findings

Quantified changes in information measures due to excitations.

Established relations between these measures and entanglement thermodynamics.

Analyzed effects for different Lifshitz dynamical exponents.

Abstract

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in $3+1$-dimensions. This geometry is the gravity dual to a class of $2+1$-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent ($z$) present in the Lifshitz field theory.