Target space entanglement entropy
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13130_2023_Article_20460.pdf
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Author(s)
Mazenc, Edward A.
Ranard, Daniel
Date Issued
March 16, 2023
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2023 Mar 16;2023(3):111
Version
Final published version
Abstract
Abstract
We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen subalgebra of observables
A
$$ \mathcal{A} $$
. The entanglement entropy is calculated as the entropy of the density matrix restricted to
A
$$ \mathcal{A} $$
. As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra
A
$$ \mathcal{A} $$
is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP03(2023)111
