Holographic duality and random tensor network
Abstract/Contents
- Abstract
- Holographic duality is a proposed correspondence between quantum many-body systems living on the conformal boundary of an asymptotically anti-de Sitter space and the quantum gravity living in one higher dimension in the bulk. A particularly interesting aspect of this duality is played by the quantum entanglement. According to the Ryu-Takayanagi formula, the entanglement entropy of a boundary region corresponds to the area of the minimal surface bounding this region, which agrees with the entropy properties of the tensor network states. This dissertation aims to build concrete relations between the holographic duality and the tensor networks. We first propose the concept of the bidirectional holographic code, which means all the boundary states can be represented in the bulk while the states within a constrained code subspace play the role of "classical geometries". We implement the bidirectional holographic code explicitly using the random tensors, which generates a class of solvable tensor network models that reproduce many properties of the holographic duality. We further generalize the random tensor network approach to allow quantum superposition of di erent spatial geometries, which moves one step towards the quantum description of the gravity theory. Lastly, we study the dynamical properties in the holographic duality using the tensor networks and find that the quantum error correction properties bridge the light-cone structure in the bulk and the buttefly velocity (i.e. the speed of chaos propagation) on the boundary.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Yang, Zhao |
|---|---|
| Associated with | Stanford University, Department of Physics. |
| Primary advisor | Qi, Xiaoliang |
| Thesis advisor | Qi, Xiaoliang |
| Thesis advisor | Hayden, Patrick, 1965- |
| Thesis advisor | Zhang, Shoucheng |
| Advisor | Hayden, Patrick, 1965- |
| Advisor | Zhang, Shoucheng |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Zhao Yang. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Zhao Yang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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