Entanglement structure in quantum many-body systems, field theories, and holography

TL;DR

This dissertation advances understanding of entanglement in complex quantum systems and holography by developing new methods to analyze entanglement structure, extending the scope beyond traditional models, and establishing novel theoretical frameworks.

Contribution

It introduces new techniques in quantum field theory, holography, and tensor networks to analyze entanglement in more general and realistic quantum systems.

Findings

Entanglement entropy expressed via renormalized two-point correlators.

Operational meaning of entanglement structure in tensor networks.

Correct prescription for AdS/BCFT with local operator quench.

Abstract

The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes toward a quantum description of our universe. Previous examinations of entanglement and holography have focused on specific classes of quantum systems due to the lack of computational techniques in field theory and the inherent limitation of holography. This dissertation informs various methods and formalisms to overcome these difficulties by extending the target quantum systems with mass and interactions, boundaries, and geometric variational ansatze. These approaches provide insights into the generalization of holography from the bottom up. This dissertation initiates a comprehensive study beyond conventional holography by establishing new techniques in quantum field theory, holography, and tensor networks. Focusing on entanglement entropy, we found it is generally expressed in terms of renormalized two-point correlators of both fundamental and composite operators. Beyond entanglement entropy, we found the operational meaning of the entanglement structure in generic tensor networks. Furthermore, we established a correct prescription for the AdS/BCFT correspondence with a local operator quench.