This paper explores how recent advances 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 on 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.
Entanglement renormalization is a combination of real space renormalization group techniques and ideas from quantum information theory that grew out of attempts to describe quantum critical points. The key message of entanglement renormalization is that the removal of local entanglement is essential for defining a proper real space renormalization group transformation for quantum states. This realization has permitted a compact description of some quantum critical points. Holographic gauge/gravity duality is the proposal that certain quantum field theories without gravity are dual to theories of quantum gravity in a curved higher dimensional "bulk" geometry. Holography provides a way to compute field theory observables from a completely different point of view using a small amount of information encoded geometrically. Real space renormalization is also important in the holographic framework, thus hinting at a possible connection between holography and entanglement renormalization.
The paper discusses how entanglement can be used to define a geometry, and how this relates to holography. It shows that the entanglement structure of a quantum state can be used to define a higher dimensional geometry, and that this geometry can be used to compute field theory observables. The paper also discusses how this framework can be used to understand quantum critical points and finite temperature states. It shows that the entanglement structure of a quantum state can be used to define a geometry, and that this geometry can be used to compute field theory observables. The paper also discusses how this framework can be used to understand quantum critical points and finite temperature states.This paper explores how recent advances 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 on 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.
Entanglement renormalization is a combination of real space renormalization group techniques and ideas from quantum information theory that grew out of attempts to describe quantum critical points. The key message of entanglement renormalization is that the removal of local entanglement is essential for defining a proper real space renormalization group transformation for quantum states. This realization has permitted a compact description of some quantum critical points. Holographic gauge/gravity duality is the proposal that certain quantum field theories without gravity are dual to theories of quantum gravity in a curved higher dimensional "bulk" geometry. Holography provides a way to compute field theory observables from a completely different point of view using a small amount of information encoded geometrically. Real space renormalization is also important in the holographic framework, thus hinting at a possible connection between holography and entanglement renormalization.
The paper discusses how entanglement can be used to define a geometry, and how this relates to holography. It shows that the entanglement structure of a quantum state can be used to define a higher dimensional geometry, and that this geometry can be used to compute field theory observables. The paper also discusses how this framework can be used to understand quantum critical points and finite temperature states. It shows that the entanglement structure of a quantum state can be used to define a geometry, and that this geometry can be used to compute field theory observables. The paper also discusses how this framework can be used to understand quantum critical points and finite temperature states.