Non-Hermitian topology driven by an identity term: An exactly solvable paradigm

• URL: http://arxiv.org/abs/2607.08469v1
• Date: Thu, 09 Jul 2026 13:27:07 GMT
• Title: Non-Hermitian topology driven by an identity term: An exactly solvable paradigm
• Abstract summary: We show that a momentum-dependent identity term actively deforms the generalized Brillouin zone under non-Hermitian skin pumping.<n>This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection.
• Score: 11.093624836836929
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An identity term in the Hamiltonian is conventionally regarded as spectrally inert-it shifts energies but does not alter eigenstate topology. We show that under non-Hermitian skin pumping, this paradigm fails: a momentum-dependent identity term actively deforms the generalized Brillouin zone, thereby challenging established topological criteria that rely on fixed complex contours. Here, by introducing spin-orbit coupling into a Hatano-Nelson chain, we present an exact analytical solution for the entire non-Hermitian eigensystem under open boundary conditions. Our solution reveals how inter-cell spin-orbit coupling, synergizing with this non-trivial identity term, induces topological edge states and robust zero modes in the complete absence of chiral symmetry. This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection, and provides a rigorous benchmark for testing topological invariants in systems with momentum-dependent identity terms.

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