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Gapped PVBS models for all species numbers and dimensions
Reviews in Mathematical Physics ( IF 1.4 ) Pub Date : 2019-03-28 , DOI: 10.1142/s0129055x19500284
Marius Lemm 1 , Bruno Nachtergaele 2
Affiliation  

Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature [Formula: see text] particle species on [Formula: see text]. The PVBS models were originally introduced as toy models for the classification of ground state phases. A crucial ingredient for this classification is the existence of a spectral gap above the ground state sector. In this work, we derive a spectral gap for PVBS models at arbitrary species number [Formula: see text] and in arbitrary dimension [Formula: see text] in the perturbative regime of small anisotropy parameters. Instead of using the more common martingale method, the proof verifies a finite-size criterion in the spirit of Knabe.

中文翻译:

适用于所有物种数量和尺寸的间隙 PVBS 模型

具有边界状态的产品真空 (PVBS) 是 Heisenberg XXZ 自旋模型的表亲,并且在 [公式:参见文本] 上具有 [公式:参见文本] 粒子种类。PVBS 模型最初是作为用于基态相分类的玩具模型引入的。这种分类的一个关键因素是在基态扇区上方存在光谱间隙。在这项工作中,我们推导出 PVBS 模型在小各向异性参数的微扰状态下任意物种数 [公式:见文本] 和任意维度 [公式:见文本] 的光谱间隙。该证明没有使用更常见的鞅方法,而是本着 Knabe 的精神验证了一个有限大小的标准。
更新日期:2019-03-28
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