Aspects of entanglement entropy for gauge theories

By Ronak M. Soni, S. Trivedi. 2015

149 citations recorded by the source corpus.

A bstractA definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories.We extend the electric centre definition of Casini, Huerta and Rosabal to the Non-Abelian case and find that it differs in an important term. We also find that the entanglement entropy does not agree with the maximum number of Bell pairs that can be extracted by the processes of entanglement distillation or dilution, and give protocols which achieve the maximum bound. Finally, we compute the topological entanglement entropy which follows from the extended Hilbert space definition and show that it correctly reproduces the total quantum dimension in a class of Toric code models based on Non-Abelian discrete groups.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9e1d37bb74064ff90376e49238016f394fe61b6e

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Citations in the corpus

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.”
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 [12] 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].”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “We’ve seen that the presence of a nontrivial central operator indicates that M is not a factor on the code subspace, which in bulk effective field theory is closely related to the presence of gauge symmetry [42, 43, 45, 59–67].”
Entanglement entropy: Holography and renormalization group (2018, background): “…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) and a nice review (Pretko, 2018). to find a pure density matrix in an enlarged Hilbert space of HA…”
Relative entropy equals bulk relative entropy (2015, background): “5 Distillable entanglement In the recent papers [46, 47] it was argued that for gauge fields, only the purely quantum part of the entanglement entropy corresponds to distillable entanglement.”