2003/05/31 by M. B. Hastings · 5 citations
Mathematics · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.69.104431
published as Phys.Rev. B69 (2004) 104431 · 14 pages, 3 figures, final version in press
arxiv created 2004/02/09 · openalex publication_date 2004/03/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalization of the Lieb-Schultz-Mattis theorem to higher-dimensional spin systems is shown. The physical motivation for the result is that such spin systems typically either have long-range order, in which case there are gapless modes, or have only short-range correlations, in which case there are topological excitations. The result uses a set of loop operators, analogous to those used in gauge theories, defined in terms of the spin operators of the theory. We also obtain various cluster bounds on expectation values for gapped systems. These bounds are used, under the assumption of a gap, to rule out the first case of long-range order, after which we show the existence of a topological excitation. Compared to the ground state, the topologically excited state has, up to a small error, the same expectation values for all operators acting within any local region, but it has a different momentum.