dorsal/arxiv
View SchemaStatistics dependence of the entanglement entropy
| Authors | M. Cramer, J. Eisert, M. B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611264 |
| URL | https://arxiv.org/abs/quant-ph/0611264 |
| DOI | 10.1103/PhysRevLett.98.220603 |
| Journal | Phys. Rev. Lett. 98, 220603 (2007) |
Abstract
The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for this entanglement for critical quasi-free fermionic and bosonic lattice systems, without resorting to numerical means. We consider the geometrical setting of D-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic - where an area-law is first proven to hold - or fermionic, extending previous findings for cubic regions. For bosonic systems with nearest neighbor interaction we prove the conjectured area-law by computing the logarithmic negativity analytically. We identify a length scale associated with entanglement, different from the correlation length. For fermions we determine the logarithmic correction to the area-law, which depends on the topology of the Fermi surface. We find that Lifshitz quantum phase transitions are accompanied with a non-analyticity in the prefactor of the leading order term.
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"abstract": "The entanglement entropy of a distinguished region of a quantum many-body\nsystem reflects the entanglement present in its pure ground state. In this\nwork, we establish scaling laws for this entanglement for critical quasi-free\nfermionic and bosonic lattice systems, without resorting to numerical means. We\nconsider the geometrical setting of D-dimensional half-spaces which allows us\nto exploit a connection to the one-dimensional case. Intriguingly, we find a\ndifference in the scaling properties depending on whether the system is bosonic\n- where an area-law is first proven to hold - or fermionic, extending previous\nfindings for cubic regions. For bosonic systems with nearest neighbor\ninteraction we prove the conjectured area-law by computing the logarithmic\nnegativity analytically. We identify a length scale associated with\nentanglement, different from the correlation length. For fermions we determine\nthe logarithmic correction to the area-law, which depends on the topology of\nthe Fermi surface. We find that Lifshitz quantum phase transitions are\naccompanied with a non-analyticity in the prefactor of the leading order term.",
"arxiv_id": "quant-ph/0611264",
"authors": [
"M. Cramer",
"J. Eisert",
"M. B. Plenio"
],
"categories": [
"quant-ph",
"cond-mat.other",
"hep-th"
],
"doi": "10.1103/PhysRevLett.98.220603",
"journal_ref": "Phys. Rev. Lett. 98, 220603 (2007)",
"title": "Statistics dependence of the entanglement entropy",
"url": "https://arxiv.org/abs/quant-ph/0611264"
},
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