论文标题
Krein-Nitility Schrieffer-Wolff转换和Bosonic Bogoliubov-De Gennes和其他Krein-Hermitian Hamiltonians的乐队接触
Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
论文作者
论文摘要
克雷因·赫米特（Krein-Hermitian Hamiltonians），即哈密顿人关于无限期的内部产品的赫米尔顿人，已经成为一类重要的非热汉顿汉密尔顿人，在物理学领域，包括单颗粒玻色粒bosonic bogoliubov-基因（BDG）汉密尔顿（BDG）汉密尔顿人（BDG）汉密尔顿人和所谓的hamiltrict $ ptric $ smmettricmmets metcemmetsmets metcemmetsmetricmed''特别是，由于最近对Boson拓扑的兴趣激增，它们吸引了相当大的审查。在这些事态发展的推动下，我们为有限尺寸的动态稳定的克雷因·赫米特人的汉密尔顿人制定了扰动的克雷因·施里夫·沃尔夫转换，为利益的子空间产生了有效的哈密顿人。有效的哈密顿人是Kerin Hermitian，对于足够小的扰动，也动态稳定。作为应用程序，我们使用这种转换来证明基于玻色粒BDG汉密尔顿人中基于编码的带触摸的分析，这些分析补充了拓扑表征。我们使用这种基于对称性和编纂的简单方法在最近感兴趣的几种材料中重新审视已知的拓扑镁带触摸。
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.
