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Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture
Open accessAbstract
We show that entanglement entropy of free fermions scales faster than area law, as opposed to the scaling ${L}^{d\ensuremath{-}1}$ for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the entanglement entropy of free fermions in any dimension $d$, $S\ensuremath{\sim}\phantom{\rule{0ex}{0ex}}c(\ensuremath{\partial}\ensuremath{\Gamma},\ensuremath{\partial}\ensuremath{\Omega}){L}^{d\ensuremath{-}1}\mathrm{log}L$ as the size of a subsystem $L\ensuremath{\rightarrow}\ensuremath{\infty}$, where $\ensuremath{\partial}\ensuremath{\Gamma}$ is the Fermi surface and $\ensuremath{\partial}\ensuremath{\Omega}$ is the boundary of the region in real space. The expression for the constant $c(\ensuremath{\partial}\ensuremath{\Gamma},\ensuremath{\partial}\ensuremath{\Omega})$ is based on a conjecture due to Widom. We prove that a similar expression holds for the particle number fluctuations and use it to prove a two sided estimate on the entropy $S$.
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Cites
Entanglement Entropy and Quantum Field Theory
Calabrese, P., & Cardy, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0405152 · Cited by 3,275
Entanglement entropy and quantum field theory
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The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Colloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
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Aspects of holographic entanglement entropy
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Metadata
- Authors
- Gioev, D., & Klich, I.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-03-14
- Volume
- 96
- Issue
- 10
- Pages
- 100503-100503
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2022894999
- Cited by
- 517
- References
- 24
- FWCI
- 13.96
- Type
- journal article
- Language
- en
- Open access
- green
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