标题： 递归谱关系与分数量子霍尔系统中的电荷与中性能隙 显示英文标题

标题： Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems

摘要： 我们考虑量子格点哈密顿量，并推导出连接连续粒子数区间的递归谱关系。 一个关系给出了电荷间隙主导中性间隙的条件。 我们在一组对称性（平移不变性、电荷和偶极子守恒）下验证了这些条件，这些对称性存在于例如周期性分数量子霍尔系统中。 因此，这种间隙主导现象，之前通过数值观察到，是由对称性施加的普遍特性。 第二个关系提供了一种新的基于粒子数的归纳法来推导谱间隙。 这些结果适用于玻色子和费米子。 显示英文摘要

摘要： We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions.