[
  {
    "id": "ARR-2026-6YFENMGGBY9PPBF1-v1",
    "type": "article",
    "title": "Many-Body Filling Turns Soft Spectral Leakage into a Maintenance Floor: Exact Filled-SSH Sum Rules and an Interaction-Stable Obstruction",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          7,
          12
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-6YFENMGGBY9PPBF1",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-6YFENMGGBY9PPBF1/versions/v1/",
    "note": "Archived manuscript; ARR-2026-6YFENMGGBY9PPBF1 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "Soft spectral filtering has a more severe effect at finite filling than in a dilute edge-mode code. We consider two odd Su-Schrieffer-Heeger (SSH) rails, fill every negative-energy orbital, and encode one additional fermion in the zero mode of either rail. The code has fixed total number and supports physical coherence. For a boundary transfer at a site with zero-mode weight w_x, the desired logical Davies line has squared matrix element w_x^2. We prove the exact many-body leakage identity W_leak^filled(x) = (1 + 2w_x - 3w_x^2)/4. At the remote boundary, w_x = Theta(zeta^(2 ell)), so the logical line is Theta(zeta^(4 ell)) while the summed particle-hole leakage tends to 1/4. This differs qualitatively from the dilute identity w_x(1 - w_x) = Theta(zeta^(2 ell)).For a Davies filter whose off-target tail is epsilon_ell = exp[-q ell + o(ell)], the bounded-latency exact-refresh power obeys the exponent law lim_(ell to infinity) -(1/ell) log P_(ell,tau) = min{4m,q}, where m = -log zeta, under explicit uniform-envelope and resource-ledger assumptions. A width-independent tail, a special case with q = 0, produces a nonzero maintenance floor rather than merely halving the membrane exponent. More generally, q = 0 means only that the decay is subexponential. Every nonzero tail also makes the exact rapid-refresh limit logarithmically singular at each fixed width.The floor is not a free-fermion accident. For arbitrary interacting number-conserving rails, we prove an exact static identity expressing leakage as a local occupation product minus the logical matrix element. Uniform finite filling and remote-edge indistinguishability force a positive leakage floor. A new local spectral-window lemma places a fixed fraction of that weight in a width-independent Bohr-frequency window using only a commutator norm. Consequently, any bath tail bounded below on that window yields an interaction-stable Davies leakage floor. Quasi-local spectral flow shows persistence in a neighborhood of a symmetry-preserving gapped SSH phase. Exact diagonalization of the interacting spinless SSH chain shows that repulsive and attractive interactions change the observed edge-localization exponent while the leakage is already driven close to 1/4 at accessible widths."
  }
]