Entanglement and alpha entropies for a massive Dirac field in two dimensions
Open accessAbstract
We present some exact results on universal quantities derived from the local density matrix ρ, for a free massive Dirac field in two dimensions. We first find tr ρ n in a novel fashion, which involves the correlators of suitable operators in the sine–Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painlevé V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c -theorem to the alpha-entropies.
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The entanglement entropy of the free Dirac fermion is given by (A.15).
“The entanglement entropy of the free Dirac fermion is given by [70]”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [70]
In the theory of c free Dirac fermions, the entanglement entropy of the region (5.6) is (5.7), where UV divergences are dropped.
“In the theory of c free Dirac fermions [49], the entanglement entropy of the region”
From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [49]
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“The entanglement entropy of the free Dirac fermion is given by [70]”
Method
- Authors
- Casini, H., Fosco, C. D., & Huerta, M.
- Affiliations
- Bariloche Atomic Centre (AR)
- Venue
- Journal of Statistical Mechanics: Theory and Experiment
- Publisher
- IOP Publishing
- Published
- 2005-07-27
- Volume
- 2005
- Issue
- 07
- Pages
- P07007-P07007
- ISSN
- 1742-5468 (ISSN-L)
- OpenAlex
- W1977928007
- Cited by
- 293
- References
- 43
- Citations by year
- 2026: 8 · 2025: 6 · 2024: 18 · 2023: 31 · 2022: 27 · 2021: 42 · 2020: 27 · 2019: 24 · 2018: 8 · 2017: 19 · 2016: 11 · 2015: 7 · 2014: 13 · 2013: 7 · 2012: 8
- FWCI
- 2.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Statistical Mechanics Theory and Experiment (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- entanglement entropy, massive Dirac field, two-dimensional field theory, sine-Gordon model, Painlevé V equation, c-theorem
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