2006/08/31 by Bruno Nachtergaele, Robert Sims · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum many-body systems #Spectral Theory in Mathematical Physics #cond-mat.str-el #math-ph #math.MP #msc:82B10 #msc:82B20 #quant-ph
paper · pdf · doi:10.1007/s00220-007-0342-z
published as Commun. Math. Phys. 276 (2007) 437--472 · final version
openalex publication_date 2007/09/08 · arxiv created 2007/12/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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, of arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (Clog L)/L. This result can be regarded as a multi-dimensional Lieb-Schultz-Mattis theorem and provides a rigorous proof of a recent result by Hastings.