dorsal/arxiv
View SchemaEntanglement entropy of fermions in any dimension and the Widom conjecture
| Authors | Dimitri Gioev, Israel Klich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504151 |
| URL | https://arxiv.org/abs/quant-ph/0504151 |
| DOI | 10.1103/PhysRevLett.96.100503 |
| Journal | Phys. Rev. Lett. 96, 100503 (2006) |
Abstract
We show that entanglement entropy of free fermions scales faster then area law, as opposed to the scaling $L^{d-1}$ 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 $d$, $S\sim c(\partial\Gamma,\partial\Omega)\cdot L^{d-1}\log L$ as the size of a subsystem $L\to\infty$, where $\partial\Gamma$ is the Fermi surface and $\partial\Omega$ is the boundary of the region in real space. The expression for the constant $c(\partial\Gamma,\partial\Omega)$ is based on a conjecture due to H. Widom. We prove that a similar expression holds for the particle number fluctuations and use it to prove a two sided estimates on the entropy $S$.
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"abstract": "We show that entanglement entropy of free fermions scales faster then area\nlaw, as opposed to the scaling $L^{d-1}$ for the harmonic lattice, for example.\nWe also suggest and provide evidence in support of an explicit formula for the\nentanglement entropy of free fermions in any dimension $d$, $S\\sim\nc(\\partial\\Gamma,\\partial\\Omega)\\cdot L^{d-1}\\log L$ as the size of a subsystem\n$L\\to\\infty$, where $\\partial\\Gamma$ is the Fermi surface and $\\partial\\Omega$\nis the boundary of the region in real space. The expression for the constant\n$c(\\partial\\Gamma,\\partial\\Omega)$ is based on a conjecture due to H. Widom. We\nprove that a similar expression holds for the particle number fluctuations and\nuse it to prove a two sided estimates on the entropy $S$.",
"arxiv_id": "quant-ph/0504151",
"authors": [
"Dimitri Gioev",
"Israel Klich"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"math.FA"
],
"doi": "10.1103/PhysRevLett.96.100503",
"journal_ref": "Phys. Rev. Lett. 96, 100503 (2006)",
"title": "Entanglement entropy of fermions in any dimension and the Widom conjecture",
"url": "https://arxiv.org/abs/quant-ph/0504151"
},
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