Entanglement vs. gap for onedimensional spin systems
Abstract
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a onedimensional system states that for the ground state, the entanglement of any interval is upperbounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap {Delta} is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small {Delta}. To help resolve this asymptotic behavior, we construct a family of onedimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/{Delta}, whereas previously studied systems had the entropy of all intervals bounded by a constant times log(1/{Delta}).
 Authors:

 Los Alamos National Laboratory
 HEBREW UNIV
 PERIMETER INSTITUTE
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 960871
 Report Number(s):
 LAUR0807721; LAUR087721
TRN: US201008%%780
 DOE Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Name: Journal of Mathematical Physics
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71; BEHAVIOR; ENTROPY; GROUND STATES; HAMILTONIANS; ONEDIMENSIONAL CALCULATIONS; POLYNOMIALS; SIZE; SPIN
Citation Formats
Hastings, Matthew, Aharonov, Dorit, and Gottesman, Daniel. Entanglement vs. gap for onedimensional spin systems. United States: N. p., 2008.
Web.
Hastings, Matthew, Aharonov, Dorit, & Gottesman, Daniel. Entanglement vs. gap for onedimensional spin systems. United States.
Hastings, Matthew, Aharonov, Dorit, and Gottesman, Daniel. Tue .
"Entanglement vs. gap for onedimensional spin systems". United States. https://www.osti.gov/servlets/purl/960871.
@article{osti_960871,
title = {Entanglement vs. gap for onedimensional spin systems},
author = {Hastings, Matthew and Aharonov, Dorit and Gottesman, Daniel},
abstractNote = {We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a onedimensional system states that for the ground state, the entanglement of any interval is upperbounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap {Delta} is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small {Delta}. To help resolve this asymptotic behavior, we construct a family of onedimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/{Delta}, whereas previously studied systems had the entropy of all intervals bounded by a constant times log(1/{Delta}).},
doi = {},
url = {https://www.osti.gov/biblio/960871},
journal = {Journal of Mathematical Physics},
number = ,
volume = ,
place = {United States},
year = {2008},
month = {1}
}