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

• URL: http://arxiv.org/abs/2606.06626v1
• Date: Thu, 04 Jun 2026 18:22:57 GMT
• Title: Non-Hermitian Crystalline Braid Topology from Hermitian Projection: A Zero-Mode Resonance Mechanism
• Abstract summary: We show that non-Hermitian crystalline braid topology can emerge from projection alone.<n>The mechanism is zero-mode-resonant projection.<n>We demonstrate this mechanism in an exactly solvable model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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