A multi-dimensional Lieb-Schultz-Mattis theorem

Bruno Nachtergaele, Robert Sims

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, with arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C log L)/L. This result can be regarded as a multi-dimensional Lieb-Schultz-Mattis theorem [14] and provides a rigorous proof of the main result in [8].

Original languageEnglish (US)
Pages (from-to)437-472
Number of pages36
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Dec 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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