Reduction of one-dimensional non-Hermitian point-gap topology by interactions
Tsuneya Yoshida, Yasuhiro Hatsugai
Abstract
In spite of extensive works on non-Hermitian topology, interaction effects remain crucial questions. We analyze correlated non-Hermitian systems with special emphasis on the one-dimensional point-gap topology. Specifically, our analysis elucidates that interactions result in a reduction of the topological classification $\mathbb{Z}\ifmmode\times\else\texttimes\fi{}\mathbb{Z}\ensuremath{\rightarrow}\mathbb{Z}$ for systems of one synthetic dimension with charge $\mathrm{U}(1)$ symmetry and spin-parity symmetry. Furthermore, we analyze an extended Hatano-Nelson chain which exhibits striking interaction effects; interactions destroy the non-Hermitian skin effect at the noninteracting level. This fragility of the non-Hermitian skin effect against interactions is consistent with the reduction of the point-gap topology in the one spatial dimension. The above discoveries shed light on the topology of correlated systems and open up different directions for research on non-Hermitian topological physics.