所有物种数量和维度的有间隙PVBS模型
Gapped PVBS models for all species numbers and dimensions
摘要：
带边界态的乘积真空（PVBS）是海森堡XXZ自旋模型的表亲，并且在$\mathbb Z^d$上具有$n$粒子种类。PVBS模型最初是作为玩具模型引入的，用于基态相的分类。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，我们得到了一个光谱间隙的PVBS模型在任意物种数$n$和任意尺寸$d$的小各向异性参数的微扰制度。而不是使用更常见的鞅方法，证明验证了有限大小的标准在Knabe的精神。
英文摘要：
Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature $n$ particle species on $\mathbb Z^d$. 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 $n$ and in arbitrary dimension $d$ 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.
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