Brian Swingle presents a novel framework that combines real-space renormalization group methods with holographic dualities in quantum gravity to define a generalized notion of holography. This framework organizes information in a quantum state based on scale and defines a higher-dimensional geometry from this structure. States with finite correlation lengths yield simple geometries, while quantum critical points produce a discrete version of anti-de Sitter space. Finite-temperature quantum states can include black hole-like objects, and the gross features of equal-time correlation functions are reproduced in this geometric framework. The relationship between this framework and established versions of holography is discussed.
The introduction highlights the need for a more general theory beyond traditional symmetry-breaking descriptions, particularly for exotic phases like the fractional quantum Hall effect. Entanglement renormalization, a combination of real-space renormalization group techniques and quantum information theory, is crucial for defining proper real-space renormalization group transformations. Holographic gauge/gravity duality suggests that certain quantum field theories without gravity are dual to theories of quantum gravity in a curved higher-dimensional bulk geometry.
The paper details the implementation of entanglement renormalization on a concrete lattice system, such as the quantum Ising model, and shows how the entanglement structure of the quantum state can be used to define a higher-dimensional geometry. This geometry is determined by the connectivity of the quantum circuit represented by the tensor network. The paper also discusses the geometrical interpretation of finite-temperature states and correlation functions, and the connection to holographic duality.
The conclusion emphasizes the framework's ability to construct an emergent holographic space from the entanglement properties of various many-body states, including free bosons, fermions, quantum critical points, and topological phases. The framework encodes the gross features of entanglement and correlation functions geometrically, both in lattice setups and within the context of gauge/gravity duality. The paper also touches on future directions, including the need for a better understanding of gauge/gravity duality and the potential for applying these ideas to more complex systems.Brian Swingle presents a novel framework that combines real-space renormalization group methods with holographic dualities in quantum gravity to define a generalized notion of holography. This framework organizes information in a quantum state based on scale and defines a higher-dimensional geometry from this structure. States with finite correlation lengths yield simple geometries, while quantum critical points produce a discrete version of anti-de Sitter space. Finite-temperature quantum states can include black hole-like objects, and the gross features of equal-time correlation functions are reproduced in this geometric framework. The relationship between this framework and established versions of holography is discussed.
The introduction highlights the need for a more general theory beyond traditional symmetry-breaking descriptions, particularly for exotic phases like the fractional quantum Hall effect. Entanglement renormalization, a combination of real-space renormalization group techniques and quantum information theory, is crucial for defining proper real-space renormalization group transformations. Holographic gauge/gravity duality suggests that certain quantum field theories without gravity are dual to theories of quantum gravity in a curved higher-dimensional bulk geometry.
The paper details the implementation of entanglement renormalization on a concrete lattice system, such as the quantum Ising model, and shows how the entanglement structure of the quantum state can be used to define a higher-dimensional geometry. This geometry is determined by the connectivity of the quantum circuit represented by the tensor network. The paper also discusses the geometrical interpretation of finite-temperature states and correlation functions, and the connection to holographic duality.
The conclusion emphasizes the framework's ability to construct an emergent holographic space from the entanglement properties of various many-body states, including free bosons, fermions, quantum critical points, and topological phases. The framework encodes the gross features of entanglement and correlation functions geometrically, both in lattice setups and within the context of gauge/gravity duality. The paper also touches on future directions, including the need for a better understanding of gauge/gravity duality and the potential for applying these ideas to more complex systems.