From local weight selection to Zeno slowdown in an open Su-Schrieffer-Heeger chain with a single local loss

Abstract

We study a quadratic open SSH chain with a single-site loss and show that the many-body fermionic Lindblad problem admits an exact reduction to a finite non-Hermitian one-body matrix with a rank-one imaginary impurity. Its rapidities generate the complete Liouvillian spectrum and reveal three mechanisms governing the slowest relaxation. At weak loss, decay is selected by the clean local spectral weight at the lossy site, yielding the generic law $Δ_{\mathcal L}\simγN^{-3}$ and, in the topological regime, exponentially smaller edge-controlled gaps. At intermediate loss, a centered bulk-loss geometry reaches an exact exceptional point on the real-$γ$ axis. Symmetry-related rapidity pairs coalesce simultaneously, including the pair at the lower rapidity edge. Exact real-space dynamics at this lower-edge exceptional point exhibits a polynomially enhanced exponential tail, whereas a matched high-energy control with the same parity-even one-body decay edge but no lower-edge defectiveness remains nearly exponential. At strong loss, one ultrafast defect mode separates from an active slow sector governed by a cut-chain Zeno problem, giving $Δ_{\mathcal L}\simγ^{-1}$ up to a geometry-dependent prefactor. The full finite fermionic Liouvillian spectrum, including its operator-parity sectors and subset-sum structure, is statistics-specific. By contrast, the elementary one-body decay spectrum and the three associated mechanisms are governed by a finite-dimensional linear drift matrix, so their spectral and dynamical signatures can also be accessed in bosonic and classical-wave platforms engineered to realize the same effective matrix. These results establish how topology, defect geometry, and local dissipation jointly organize long-time relaxation in an open dimerized lattice.