Krein-unitary Schriff-Wolff变换和玻色子Bogoliubov-de Gennes及其它Krein-Hermitian哈密顿量中的带接触
Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
摘要：
Krein-Hermitian Hamilton，即关于不定内积的厄米哈密顿量，已经成为物理学中一类重要的非厄米哈密顿量，包括单粒子玻色子Bogoliubov-de Gennes（BdG）哈密顿量和所谓的“$PT$ -对称”非厄米哈密顿量。特别是，由于最近对玻色子拓扑的兴趣激增，它们吸引了相当多的审查。受这些发展的启发，我们制定了一个微扰的Krein酉Schriling-Wolff变换有限大小的动态稳定的Krein-Hermitian哈密顿，产生一个有效的哈密顿子空间的利益。有效的哈密顿量是克莱因厄米特的，并且对于足够小的扰动，也是动态稳定的。作为一个应用程序，我们使用这种变换来证明余维为基础的分析带接触玻色子BdG哈密顿，补充拓扑特征。我们使用这种简单的方法的对称性和余维的基础上，重新审视已知的拓扑磁振子带接触最近感兴趣的几种材料。
英文摘要：
Krein-Hermitian Hamiltonians, i.e., Hamiltonians Hermitian with respect to an indefinite inner product, have emerged as an important class of non-Hermitian Hamiltonians in physics, encompassing both single-particle bosonic Bogoliubov-de Gennes (BdG) Hamiltonians and so-called "$PT$-symmetric" non-Hermitian Hamiltonians. In particular, they have attracted considerable scrutiny owing to the recent surge in interest for boson topology. Motivated by these developments, we formulate a perturbative Krein-unitary Schrieffer-Wolff transformation for finite-size dynamically stable Krein-Hermitian Hamiltonians, yielding an effective Hamiltonian for a subspace of interest. The effective Hamiltonian is Krein Hermitian and, for sufficiently small perturbations, also dynamically stable. As an application, we use this transformation to justify codimension-based analyses of band touchings in bosonic BdG Hamiltonians, which complement topological characterization. We use this simple approach based on symmetry and codimension to revisit known topological magnon band touchings in several materials of recent interest.
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