Entanglement in Quantum Field Theory and Holography

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.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.

arXiv:2308.09758Aug 18, 20230 citations

Universality of Magic in Local Quantum Field Theory

Valentin Benedetti, Atish Dabholkar, Marcello Dalmonte

We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances. The argument rests on the fact that the entanglement spectrum is flat for stabilizer states but non-flat for cyclic and separating states in a local QFT as a consequence of the type III $_1$ nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances. The argument rests on the fact that the entanglement spectrum is flat for stabilizer states but non-flat for cyclic and separating states in a local QFT as a consequence of the type III$_1$ nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.

hep-thCross-listedarXiv:2607.16403Jul 21, 20260 citations

Aspects of entanglement in holography, harmonic lattices and non-relativistic quantum field theories

Francesco Gentile

This thesis presents three studies elucidating aspects of entnaglement entropy in holography, harmonic lattices and non-realtivistic quantum field theory. In the first part we review the geodesic bit thread forumlation for holographic entanglement entropy and show that in presence of an event horizon we can recover the holographic thermal entropy. In the second part we study the entanglement hamiltonian for a two-interval system in a harmonic lattice, in both the massless and super massive limit. In the third part we study the symmetry resolved entanglement entropies in a Schrodinger fermionic field theory.This thesis presents three studies elucidating aspects of entnaglement entropy in holography, harmonic lattices and non-realtivistic quantum field theory. In the first part we review the geodesic bit thread forumlation for holographic entanglement entropy and show that in presence of an event horizon we can recover the holographic thermal entropy. In the second part we study the entanglement hamiltonian for a two-interval system in a harmonic lattice, in both the massless and super massive limit. In the third part we study the symmetry resolved entanglement entropies in a Schrodinger fermionic field theory.

Dec 18, 20250 citations

Quantum holography—the paradigm of quantum entanglement

Peter J. Marcer, Walter Schempp

International Conference on Computing Anticipatory Systems (CASYS)Jan 1, 19996 citations

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nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.