Momentum-space entanglement and renormalization in quantum field theory

By Vijay Balasubramanian, Michael B. McDermott, Mark Van Raamsdonk. 2011

182 citations recorded by the source corpus.

The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation between this density matrix and the conventional Wilsonian effective action. We argue that the entanglement entropy of and mutual information between subsets of field theoretic degrees of freedom at different momentum scales are natural observables in quantum field theory and demonstrate how to compute these in perturbation theory. The results may be understood heuristically based on the scale-dependence of the coupling strength and number of degrees of freedom. We measure the rate at which entanglement between degrees of freedom declines as their scales separate and suggest that this decay is related to the property of decoupling in quantum field theory.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/79ff94ffe5d780edb4d290f958d12dcd7d1fc813

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. T. Takayanagi
3. H. Casini
4. Ling-Yan Hung
5. J. Boer
6. David Blanco
7. B. Czech
8. Vijay Balasubramanian

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. Ling-Yan Hung
4. H. Casini
5. J. Boer
6. V. Hubeny
7. M. Rangamani
8. T. Nishioka

Citations in the corpus

• Entanglement entropy from a holographic viewpoint (2012, background): “1 Recently, the entanglement entropy for the subsystem A by a region in the momentum space has been analyzed in [27].”
• On the architecture of spacetime geometry (2012, background): “Further, we might note that there has already been some speculation that evaluating this expression on other surfaces in the bulk geometry may yield interesting entropic measures of entanglement in the boundary theory [9, 10].”
• Relative entropy and holography (2013, background): “Further, it has provided new insights on the structure of renormalization group flows [4, 5].”
• Bulk curves from boundary data in holography (2013, background): “Some types of UV-IR entanglement were studied previously in [20].”