无序玻色系统的拓扑边态
Topological edge states for disordered bosonic systems
摘要：
单粒子希尔伯特空间上的二次玻色哈密顿量可以用粒子-空穴希尔伯特空间上的Bogoliubov-de Gennes（BdG）哈密顿量来描述。一般来说，BdG哈密顿量不是自共轭的，而只是$J$ -自共轭的粒子-空穴空间视为Krein空间。然而，它的能带可以有非平凡的拓扑不变量，如陈数或缠绕数。通过对紧束缚模型的深入分析，证明了这些不变量导致了对一大类可能的无序扰动具有鲁棒性的玻色边缘模。此外，一般情况下，这些边缘状态是动态不稳定的，即使批量模式是稳定的。
英文摘要：
Quadratic bosonic Hamiltonians over a one-particle Hilbert space can be described by a Bogoliubov-de Gennes (BdG) Hamiltonian on a particle-hole Hilbert space. In general, the BdG Hamiltonian is not selfadjoint, but only $J$-selfadjoint on the particle-hole space viewed as a Krein space. Nevertheless, its energy bands can have non-trivial topological invariants like Chern numbers or winding numbers. By a thorough analysis for tight-binding models, it is proved that these invariants lead to bosonic edge modes which are robust to a large class of possibly disordered perturbations. Furthermore, general scenarios are presented for these edge states to be dynamically unstable, even though the bulk modes are stable.
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