Holographic study of entanglement and complexity for mixed states

Saha, Ashis; Gangopadhyay, Sunandan

doi:10.48550/arxiv.2101.00887

Cited by 1 publication

(1 citation statement)

References 50 publications

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“…Unlike mutual information, the entanglement of purification requires further input besides entanglement entropy and thus it is an interesting quantity to study holographically. Both, mutual information and entanglement of purification have been successfully used to characterize strongly coupled phases of matter, including finite density states and quantum critical systems [90][91][92][93][94][95][96][97][98][99][100][101][102][103][104].…”

Section: Information Theoretic Probes Of Fractionalized Statesmentioning

confidence: 99%

Quantum information probes of charge fractionalization in large-$N$ gauge theories

DiNunno,

Jokela,

Pedraza

et al. 2021

Preprint

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We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into a fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To overcome this challenge, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U (1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

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