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arXiv · 2607.08469

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

Lingfang Li·Yating Wei·Yang Ruan·Gangzhou Wu·Jun Wang·Shihua Chen·Tong Lin·Ching Hua Lee·Zhenhua Ni
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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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Lingfang Li, Yating Wei, Yang Ruan, Gangzhou Wu, Jun Wang, Shihua Chen, Tong Lin, Ching Hua Lee, Zhenhua Ni. 2026-07-09. Non-Hermitian topology driven by an identity term: An exactly solvable paradigm. https://arxiv.org/abs/2607.08469

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