Geometric and topological obstructions to global proper Hermitianization in quasi-Hermitian quantum systems
Year: 2026
Type: article
Abstract: Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an instantaneous algebraic Hermitianization can be obtained locally from a positive metric operator, a stronger requirement is needed for dynamical equivalence: the similarity transformation must be proper, globally single-valued, and compatible with the modified quasi-Hermitian Schrodinger equation. We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies around non-contractible loops in parameter space. We derive explicit criteria for these obstructions and illustrate them with concrete examples. Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems, clarifying when they can be globally reduced to Hermitian ones and when intrinsic non-Hermitian features persist.
DOI: 10.1103/ct62-ty8j
Authors: Ming-Zhang Wang, Xu-Yang Hou, Hao Guo
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G4680217812, G4987775540, G5319790424
OpenAlex ID: W7160652503