Entanglement Renormalization and Holography

TL;DR

This paper proposes a novel approach to holography using real space renormalization group methods, linking quantum states' scale organization to higher dimensional geometries, including AdS spaces and black hole analogs.

Contribution

It introduces a generalized holographic framework based on organizing quantum information by scale, connecting renormalization group techniques with holographic dualities.

Findings

States at quantum critical points resemble discrete AdS space

Finite temperature states can include black hole-like features

Correlation functions are reproduced by the geometric model

Abstract

I show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The generalization is based upon organizing information in a quantum state in terms of scale and defining a higher dimensional geometry from this structure. While states with a finite correlation length typically give simple geometries, the state at a quantum critical point gives a discrete version of anti de Sitter space. Some finite temperature quantum states include black hole-like objects. The gross features of equal time correlation functions are also reproduced in this geometric framework. The relationship between this framework and better understood versions of holography is discussed.