Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems

In our previous work, we established a non-Bloch band theory in one-dimensional tight-binding non-Hermitian systems [1,2]. We show a way to determine the generalized Brillouin zone for the complex Bloch wave number in a large open chain. In our recent work, we construct the non-Bloch band theory in bosonic Bogoliubov-de Gennes (BdG) systems. By using our theory, one can investigate general non-Hermitian properties in bosonic BdG systems with open boundary conditions in the thermodynamic limit. In this story, we find rich aspects of the non-Hermitian skin effect, i.e. infinitesimal instability and reentrant behavior in the bosonic Kitaev-Majorana chain. [1] K. Yokomizo and S. Murakami, Phys. Rev. Lett. 123, 066404 (2019). [2] K. Yokomizo and S. Murakami, Phys. Rev. Research 2, 043045 (2020).