发表机构
Harvard University; Kutztown University of Pennsylvania; Stony Brook University（哈佛大学; 宾夕法尼亚库兹敦大学; 石溪大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究小型圆柱和环形晶格在标量规范势下的光谱与量子态，发现规范依赖的能级交叉和简并，环形晶格出现局域化-离域化转变。
AI 中文摘要
我们研究了具有圆柱形和环形拓扑结构的小型晶格在标量规范势作用下的光谱和量子态，该规范势在格点间耦合中引入了依赖于位置的相位。由于周期性边界条件，无限晶格中假设的规范等价性通常会丧失，我们确定了恢复等价性的条件。我们追踪了各种系统参数的影响，包括规范选择、边界条件、格点间耦合强度以及附加的轴向场。我们发现了依赖于规范的能级避让交叉和持续简并，并展示了它们对相关本征态的影响。较小的晶格在光谱线中会出现与边缘态相关的显著间隙，这些间隙在热力学极限下被抑制。环形晶格具有圆柱形晶格中观察到的大多数特征的对应物，但值得注意的是，它们表现出由场参数与晶格位数之间的关系决定的从局域化到离域化的转变。
英文摘要
We examine the spectrum and quantum states of small lattices with cylindrical and toroidal topology subject to a scalar gauge potential that introduces a position dependent phase in the inter-site coupling. Equivalency of gauges assumed in infinite lattices is generally lost due to the periodic boundary conditions, and conditions that restore it are identified. We trace the impact of various system parameters including gauge choice, boundary conditions and inter-site coupling strengths, and an additional axial field. We find gauge dependent appearance of avoided crossings and persistent degeneracies, and we show their impact on the associated eigenstates. Smaller lattices develop prominent gaps in spectral lines associated with edge states, which are suppressed in the thermodynamic limit. Toroidal lattices have counterparts of most of the features observed in cylindrical lattices, but notably they display a transition from localization to delocalization determined by the relation between the field parameter and the number of lattice sites.
Comments12 pages, 11 figures
Journal refJ. Phys. B: At. Mol. Opt. Phys. 57 205301 (2024)
