Entanglement vs. gap for one-dimensional spin systems

Journal Article · Tue Jan 01 04:00:00 EST 2008 · Journal of Mathematical Physics

OSTI ID:960871

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

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1. Los Alamos National Laboratory
2. HEBREW UNIV
3. PERIMETER INSTITUTE

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}).

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 960871
• Report Number(s): LA-UR-08-07721; LA-UR-08-7721
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEHAVIOR
ENTROPY
GROUND STATES
HAMILTONIANS
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
SIZE
SPIN