Lie-Schwinger Block-Diagonalization and Gapped Quantum Chains
Lie-Schwinger Block-Diagonalization and Gapped Quantum Chains
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DOI：
10.1007/s00220-019-03613-2
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发表时间：
2020-03-20
影响因子：
2.4
通讯作者：
Pizzo, A.
中科院分区：
文献类型：
--
作者：
Frohlich, J.;Pizzo, A.
我们研究了这样的量子链，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，该哈密顿量不耦合位于链的不同位置的自由度，并且在其基态能量之上具有严格的正能量间隙。我们证明了，当耦合常数值很小时，扰动哈密顿量在基态能量以上的谱隙在链的长度上均匀地由一个正常数从下限定。在我们的证明中，我们使用了一种新的方法，该方法基于与链的连通子集相关的哈密顿算子的局部Lie-Schwinger共轭。
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.