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Title: Entanglement vs. gap for one-dimensional spin systems

Abstract

We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded 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 one-dimensional 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:
 [1];  [2];  [3]
  1. Los Alamos National Laboratory
  2. HEBREW UNIV
  3. 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):
LA-UR-08-07721; LA-UR-08-7721
TRN: US201008%%780
DOE Contract Number:  
AC52-06NA25396
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; ONE-DIMENSIONAL CALCULATIONS; POLYNOMIALS; SIZE; SPIN

Citation Formats

Hastings, Matthew, Aharonov, Dorit, and Gottesman, Daniel. Entanglement vs. gap for one-dimensional spin systems. United States: N. p., 2008. Web.
Hastings, Matthew, Aharonov, Dorit, & Gottesman, Daniel. Entanglement vs. gap for one-dimensional spin systems. United States.
Hastings, Matthew, Aharonov, Dorit, and Gottesman, Daniel. Tue . "Entanglement vs. gap for one-dimensional spin systems". United States. https://www.osti.gov/servlets/purl/960871.
@article{osti_960871,
title = {Entanglement vs. gap for one-dimensional 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 one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded 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 one-dimensional 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}
}