Institute for Mathematical Physics a Multi–dimensional Lieb–schultz–mattis Theorem a Multi-dimensional Lieb-schultz-mattis Theorem
Institute for Mathematical Physics a Multi–dimensional Lieb–schultz–mattis Theorem a Multi-dimensional Lieb-schultz-mattis Theorem
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数学物理研究所 多维 Lieb-schultz-mattis 定理 多维 Lieb-schultz-mattis 定理
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通讯作者：
Robert Sims
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作者：
B. Nachtergaele;Robert Sims
对于一类具有半整数自旋的有限程量子自旋模型，我们证明了基态的唯一性意味着低激发态的存在。对于任意有限维的线性尺寸L的系统，我们获得了激发能的上限（即，基态上方的差距）的形式（C log L）/L。这个结果可以看作是一个多维Lieb-Schultz-Mattis定理[7]，并为[4]中的主要结果提供了严格的证明.
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 (C log L)/L. This result can be regarded as a multi-dimensional Lieb-Schultz-Mattis theorem [7] and provides a rigorous proof of the main result in [4].