We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.

中文翻译：

---

Lie-Schwinger 块对角化和有隙量子链

我们研究了量子链，其哈密顿量是由哈密顿量的短程有界相互作用引起的扰动，哈密顿量不耦合位于链不同位置的自由度，并且在其基态能量之上具有严格的正能隙。我们证明，对于耦合常数的小值，其基态能量以上的扰动哈密顿量的光谱间隙从下方由链长度均匀的正常数限制。在我们的证明中，我们使用了一种基于与链的连接子集相关的哈密顿量的局部 Lie-Schwinger 共轭的新方法。