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arXiv:2607.10218

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

Y. T. Wang, X. Z. Zhang

quant-phSubmitted Jul 11, 2026• Announced Jul 14, 2026• 0 citations
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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.

Comments
23 pages, 5 figures (accepted by Physical Review A)

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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 ΔL∼γN−3Δ_{\mathcal L}\simγN^{-3}ΔL​∼γN−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-γγγ 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 ΔL∼γ−1Δ_{\mathcal L}\simγ^{-1}ΔL​∼γ−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.
The Su-Schrieffer-Heeger (SSH) chain provides a particularly stringent setting for variational quantum simulation because exact solvability, symmetry-protected topology, and boundary localized zero-mode physics coexist in a single analytically controlled lattice Hamiltonian. In this work, we use the open SSH chain as a one-particle benchmark for the Variational Quantum Eigensolver (VQE) and develop a two-part variational treatment that separately addresses its low-lying bulk spectrum and its topological near-zero sector. For the bulk benchmark, we restrict the SSH model to the one-particle sector, where the Hamiltonian reduces to an N times N hopping matrix that is encoded as a qubit operator for variational simulation. We compare three shallow variational families: a problem-aligned fermionic ansatz, a hardware-efficient ansatz, and a two-local baseline. Across the reported system sizes, the fermionic ansatz reproduces the benchmarked exact-diagonalization levels most faithfully, while the remaining circuits exhibit larger and more persistent deviations, particularly for the second reported level. These results demonstrate (in a controlled topological setting) that shallow variational accuracy depends strongly on whether the circuit manifold reflects the fermionic and lattice structure of the target Hamiltonian. We then turn to the central topological feature of the open SSH chain, namely the finite-size near-zero pair associated with exponentially localized edge states. Since these states are not extremal eigenvalues of the original Hamiltonian, they are not isolated naturally by VQE. To access this sector, we construct a folded-spectrum workflow based on the squared Hamiltonian, use variational minimization and deflation to identify the corresponding low-|E| subspace, and recover the signed near-zero energies by explicit orthonormalization and projection onto the original SSH Hamiltonian. The reconstructed pair agrees with the results of exact diagonalization and reproduces the expected exponential suppression of the finite-size splitting with increasing chain length. Taken together, the results establish a variational route to both the benchmarked bulk spectrum and the topological near-zero sector of a canonical one-dimensional topological Hamiltonian. More broadly, they show that in variational quantum simulation of topological systems, accuracy depends not only on ansatz compatibility with the Hamiltonian structure, but also on whether the chosen variational objective isolates the spectral feature of interest.
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We identify anomalous scale-free localization and associated impurity-induced loss bursts in a non-Hermitian dissipative cross-stitch lattice. By a local basis rotation, the model is mapped onto an effective non-Hermitian Su-Schrieffer-Heeger lattice, where local impurities act as tunable effective boundaries. For the parameter choice considered here, the impurity-free periodic-boundary-condition point is reached at η=1η=1η=1. Tuning ηηη away from this point drives the system through generalized-boundary-condition regimes toward two effective open-boundary-condition-like limits at η→0η\to0η→0 and η→∞η\to\inftyη→∞. For finite η∉{0,1}η\notin\{0,1\}η∈/{0,1}, the loop-sector spectra remain separated from the real-energy axis, while the corresponding eigenstates exhibit scale-free localization pinned by the impurity. Unlike conventional impurity-induced scale-free localization, the Lyapunov exponent depends explicitly on the eigenenergy, making the localization strength eigenstate dependent. We further show that this anomalous eigenmode structure produces an impurity-induced loss burst: The long-time integrated dissipation probability develops a pronounced local enhancement relative to the surrounding background near an impurity-generated effective boundary, even when the initial wave packet is prepared far away. In the single-impurity case, the burst region consists of the impurity site and its adjacent effective-boundary site, and the effect occurs without imaginary-gap closing. For multiple impurities, local burst regions emerge around all impurities, while the dominant burst boundary is selected by the initial wave-packet position and the nonreciprocal drift direction. These results connect anomalous scale-free localization with controllable dissipation dynamics in non-Hermitian lattices.
We study relaxation spectra of a quadratic spinless--fermion helical chain with an Aubry--Andre--type quasiperiodic potential and a single N--th neighbor (helical) hopping. Dissipation and pumping are introduced via local linear Lindblad jump operators and treated exactly using the third--quantization / Majorana covariance formalism. Focusing on periodic boundary conditions (to avoid edge artefacts) we compute the Liouvillian rapidities and their smallest nonzero real part (the rapidity gap) for several spatial dissipation patterns: uniform (all), single--site (one--site) and two--site (two--site) placement, plus pairwise gain/loss on helical partner sites. We show that uniform dissipation yields large, weakly lambda--dependent gaps, while sparse local dissipation produces gaps that shrink rapidly as the quasiperiodic potential lambda induces localization. Increasing t_N enhances relaxation by improving mode overlap with dissipative channels. Finite--size scaling, rapidity level statistics (Poisson vs Wigner--Dyson), and spatial profiles of slow modes provide a consistent picture linking Liouvillian spectral structure to transport and localization. Our results highlight Liouvillian rapidities as compact, experimentally relevant diagnostics of relaxation and sensitivity in engineered open quantum lattices.
Exceptional points (EPs), indicative of parity-time (PT) symmetry breaking, play a central role in non-Hermitian physics, yet most studies begin from deliberately engineered effective Hamiltonians whose parameters are tuned to exhibit exceptional behavior. In realistic open quantum systems, however, dynamics are governed by Lindblad superoperators whose spectral structure is high-dimensional, symmetry-constrained, and not obviously reducible to minimal non-Hermitian models. A general framework for discovering exceptional dynamics directly from microscopic dissipative models has been lacking. Here we introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator. Correlated dissipation induces graph symmetries that decompose Liouville space into low-dimensional invariant sectors, within which minimal non-Hermitian blocks govern the onset of EPs and PT-breaking behavior. We further introduce a numerical diagnostic - the exceptional-point strength E\mathcal{E}E - based on eigenvector conditioning, which quantifies proximity to defective dynamics without requiring analytic reduction. Applied to tight-binding models with correlated dephasing and relaxation, the method reproduces analytically predicted exceptional seams and reveals universal scaling of E\mathcal{E}E near EP manifolds. More broadly, the framework enables systematic discovery of hidden exceptional structure in complex or high-dimensional open systems and is naturally compatible with matrix-free and tensor-network implementations for scalable many-body applications.