dorsal/arxiv
View SchemaGeneral entanglement scaling laws from time evolution
| Authors | Jens Eisert, Tobias J. Osborne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603114 |
| URL | https://arxiv.org/abs/quant-ph/0603114 |
| DOI | 10.1103/PhysRevLett.97.150404 |
| Journal | Phys. Rev. Lett. 97, 150404 (2006) |
Abstract
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and making use of the powerful tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions whose geometric entropy scales logarithmically with block length. Implications for the classical simulatability are outlined.
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"abstract": "We establish a general scaling law for the entanglement of a large class of\nground states and dynamically evolving states of quantum spin chains: we show\nthat the geometric entropy of a distinguished block saturates, and hence\nfollows an entanglement-boundary law. These results apply to any ground state\nof a gapped model resulting from dynamics generated by a local hamiltonian, as\nwell as, dually, to states that are generated via a sudden quench of an\ninteraction as recently studied in the case of dynamics of quantum phase\ntransitions. We achieve these results by exploiting ideas from quantum\ninformation theory and making use of the powerful tools provided by\nLieb-Robinson bounds. We also show that there exist noncritical fermionic\nsystems and equivalent spin chains with rapidly decaying interactions whose\ngeometric entropy scales logarithmically with block length. Implications for\nthe classical simulatability are outlined.",
"arxiv_id": "quant-ph/0603114",
"authors": [
"Jens Eisert",
"Tobias J. Osborne"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"math-ph",
"math.MP"
],
"doi": "10.1103/PhysRevLett.97.150404",
"journal_ref": "Phys. Rev. Lett. 97, 150404 (2006)",
"title": "General entanglement scaling laws from time evolution",
"url": "https://arxiv.org/abs/quant-ph/0603114"
},
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