半空间上$d$维PVBS模型的谱隙和边激发
Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces
摘要：
本文分析了一类定义在超平面上的$d$维超立方晶格半空间上的量子自旋模型，超平面的法向量是向内的$m\in\mathbb{R}^d$。该系列模型先前被引入为具有边界状态的单物种乘积粒子（PVBS）模型，其是具有XXZ型最近邻相互作用的自旋$1/2$模型，该模型取决于参数$λ_j\in (0,\infty)$，每个参数用于每个坐标方向。对于任何给定的参数值，我们证明了这些模型的独特的基态以上的光谱间隙的上限，这正好是一个方向的正常矢量$m$消失。对于所有其他选择的$m$，我们得到了一个积极的下限的频谱间隙，除了情况$λ_1 =\cdots =λ_d=1$，这是已知的无隙激发的散装。
英文摘要：
We analyze a class of quantum spin models defined on half-spaces in the $d$-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector $m\in\mathbb{R}^d$. The family of models was previously introduced as the single species Product Vacua with Boundary States (PVBS) model, which is a spin-$1/2$ model with a XXZ-type nearest neighbor interactions depending on parameters $λ_j\in (0,\infty)$, one for each coordinate direction. For any given values of the parameters, we prove an upper bound for the spectral gap above the unique ground state of these models, which vanishes for exactly one direction of the normal vector $m$. For all other choices of $m$ we derive a positive lower bound of the spectral gap, except for the case $λ_1 =\cdots =λ_d=1$, which is known to have gapless excitations in the bulk.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
