Entanglement vs. gap for one-dimensional spin systems

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

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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:

Hastings, Matthew ^[1]; Aharonov, Dorit ^[2]; Gottesman, Daniel ^[3]

Los Alamos National Laboratory
HEBREW UNIV
PERIMETER INSTITUTE

Publication Date:: 2008-01-01

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

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                    Hastings, Matthew, Aharonov, Dorit, and Gottesman, Daniel. Entanglement vs. gap for one-dimensional spin systems.  United States: N. p., 2008. 
        Web.

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                    Hastings, Matthew, Aharonov, Dorit, & Gottesman, Daniel. Entanglement vs. gap for one-dimensional spin systems.  United States.

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                    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.

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@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}

}

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