Persistence of Exponential Decay and Spectral Gaps for Interacting Fermions
Persistence of Exponential Decay and Spectral Gaps for Interacting Fermions
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DOI：
10.1007/s00220-018-3211-z
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发表时间：
2019-01-01
影响因子：
2.4
通讯作者：
Salmhofer, Manfred
中科院分区：
文献类型：
--
作者：
De Roeck, Wojciech;Salmhofer, Manfred
我们考虑格点上的弱相互作用费米子系统。相应的自由费米子系统被假定为具有一个基态，该基态与光谱的其余部分被一个间隙隔开。我们证明，如果相互作用和自由哈密顿量是足够快的衰减项的总和，如果相互作用是足够弱的，那么相互作用系统有一个光谱间隙，以及，均匀的晶格尺寸。我们的方法依赖于收敛的费米子微扰理论，从而为Hastings最近使用的方法提供了一种替代方法（自由费米哈密顿的稳定性，arXiv：1706.02270，2017），并将结果扩展到包括非自伴相互作用项。
We consider systems of weakly interacting fermions on a lattice. The corresponding free fermionic system is assumed to have a ground state separated by a gap from the rest of the spectrum. We prove that, if both the interaction and the free Hamiltonian are sums of sufficiently rapidly decaying terms, and if the interaction is sufficiently weak, then the interacting system has a spectral gap as well, uniformly in the lattice size. Our approach relies on convergent fermionic perturbation theory, thus providing an alternative method to the one used recently by Hastings (The stability of free Fermi hamiltonians, arXiv:1706.02270, 2017), and extending the result to include non-selfadjoint interaction terms.