Approximating the ground state of gapped quantum spin systems

Eman Hamza, Spyridon Michalakis, Bruno Nachtergaele, Robert Sims

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Zd. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset XV the ground state projector can be approximated by the product of two projections, one supported on X and one supported on Xc, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. This result generalizes to multidimensional models, a result of Hastings that was an important part of his proof of an area law in one dimension ["An area law for one dimensional quantum systems," J. Stat. Mech.: Theory Exp. 2007, 08024].

Original languageEnglish (US)
Article number095213
JournalJournal of Mathematical Physics
Issue number9
StatePublished - 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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