Non-Hermitian Crystalline Braid Topology from Hermitian Projection: A Zero-Mode Resonance Mechanism

Abstract:Non-Hermitian topological phases are usually engineered through gain, loss, asymmetric couplings, or explicit environmental channels. Here we show that non-Hermitian crystalline braid topology can instead emerge from projection alone, starting from a fully Hermitian and topologically trivial parent lattice. The mechanism is zero-mode-resonant projection. When the eliminated complement is zero-mode free, projection has a smooth low-frequency limit and reduces to a static Schur complement, yielding conventional SSH-type descendants. When a complement zero mode couples to the retained subsystem, the embedding self-energy develops a pole, the zero-frequency limit becomes singular, and topology is carried by the finite-frequency projected Green's function-where frequency is a tunable parameter, the drive frequency in a circuit realization, for instance. We demonstrate this mechanism in an exactly solvable model, a trivial nearest-neighbor square lattice with an embedded one-dimensional zig-zag brane. Odd-parity periodic sectors are resonant: a sublattice-imbalance zero mode generates the singular self-energy, and the complex spectrum forms an abelian two-band braid whose transitions occur only at isolated finite frequencies. Although the internal class is $\text{AI}^†$ featuring only trivial phases, embedding parity induces conjugated pseudo-Hermiticity (CPH), quantizes the complex Berry phase, and identifies it with the braid count. The model is free of the non-Hermitian skin effect, making the invariant a genuine Bloch bulk quantity. In topolectrical realizations, the same finite-frequency braid transitions appear as transmission zeros and admittance features at the predicted drive frequencies.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2606.06626 [cond-mat.mes-hall]

(or arXiv:2606.06626v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2606.06626 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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