Symmetry-based classification of non-Bloch bands under open boundary conditions

Determine the role of symmetries in the topological classification of non-Bloch bands of non-Hermitian multiband systems under open boundary conditions, specifically whether and how symmetry constraints refine or extend the homotopy and braiding-topology characterization of open-boundary energy bands associated with generalized Brillouin zones (sub-GBZs).

Background

The paper develops a continuity criterion and a homotopy-based braiding-topology framework for non-Bloch bands of non-Hermitian systems under open boundary conditions, including multiband cases with sub-GBZs. This characterization focuses on band vorticity and braid-group structures, and is constructed without invoking symmetry constraints.

In the conclusions, the authors explicitly point out that their analysis does not rely on symmetry assumptions. They then highlight as an open question how symmetries (e.g., crystalline or antiunitary symmetries that are known to affect non-Hermitian topology under periodic boundaries) might participate in and further refine the topological classification of non-Bloch bands under open boundaries. Addressing this would connect the proposed braiding-topology characterization with symmetry-protected or symmetry-enriched classifications in the broader non-Hermitian band-theory literature.