Lie-Schwinger块对角化与带隙量子链
Lie-Schwinger block-diagonalization and gapped quantum chains
摘要：
我们研究量子链，其汉密尔顿量是由汉密尔顿量的短程有界相互作用引起的扰动，该汉密尔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正的能隙。我们证明了，对于小的值的耦合常数，频谱间隙的扰动哈密顿量以上的基态能量是有界的从下面由一个正的常数均匀的链的长度。在我们的证明中，我们使用一种新的方法的基础上，当地的李-施温格共轭的哈密尔顿与连接的子集链。
英文摘要：
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.
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