On the entanglement entropy for gauge theories

By Sudip Ghosh, Ronak M. Soni, S. Trivedi. 2015

181 citations recorded by the source corpus.

A bstractWe propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤN$$ {\mathbb{Z}}_N $$ and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.

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

View Paper: https://www.semanticscholar.org/paper/c519cbc9613e9d9ef3f2860b3e88d7e237fbb30f

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. L. Freidel
2. S. Raju
3. T. Nishioka
4. William Donnelly
5. H. Geng
6. A. Karch
7. S. Trivedi
8. Ronak M. Soni

In Nuclear and High Energy Physics

1. S. Raju
2. T. Nishioka
3. T. Takayanagi
4. H. Geng
5. A. Karch
6. L. Freidel
7. Sanjit Shashi
8. Marcos Riojas

In Statistical and Nonlinear Physics

1. S. Raju
2. L. Freidel
3. S. Trivedi
4. William Donnelly
5. Ronak M. Soni
6. T. Nishioka
7. A. Karch
8. H. Geng

Citations in the corpus

• Circuit complexity in fermionic field theory (2018, background): “The question of gauge invariance on the other hand seems like one where substantial progress might not be too hard to make: perhaps an approach along the lines of [10] which uses Wilson line based variables to define entanglement entropy might be useful here as well for non-Abelian gauge theories.”
• Local subsystems in gauge theory and gravity (2016, methodology): “Instead we will follow an approach that has been called the extended Hilbert space construction [17–21].”
• Inconsistency of islands in theories with long-range gravity (2021, background): “3When the boundary theory is a gauge theory, these algebras have a center [69, 70].”
• Lessons from the information paradox (2020, background): “Even in a gauge theory, the algebra of operators associated with a region has a nontrivial center [54–57], and so there is some ambiguity in how to divide up the set of local operators between a region and its complement.”
• Aspects of entanglement entropy for gauge theories (2015, background): “It was shown in [2] and [1] that the electric centre choice of CHR leads to a definition of entanglement entropy that coincides with the extended Hilbert space definition given above in the Abelian case.”
• Entanglement entropy: Holography and renormalization group (2018, background): “…entropy in gauge theories, see e.g. (Aoki et al., 2015; Casini et al., 2014; Chen et al., 2015; Donnelly, 2014; Donnelly and Wall, 2015, 2016; Ghosh et al., 2015; Hung and Wan, 2015; Ma, 2016; Pretko and Senthil, 2016; Radicevic, 2014, 2016; Soni and Trivedi, 2016; Van Acoleyen et al., 2016)…”