{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3808bb406a520f3e4a3e3d59adf4e1640971ed0a73be17f26f77944446437830","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3103d72cf266c15f70611abb9e375dd26cc418d19c86bb08962d1d8f26f691ef","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.monitored-circuits.monitored-free-fermions-1d","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"For particles that do not interact, some simulations show a whole range of measurement rates with slowly growing entanglement, while a field theory predicts that this range disappears in very large systems. The two pictures disagree.","posed_since":"2021","precise":"For 1D free fermions with particle-number conservation under random projective (or continuous weak) measurements of local occupation numbers at rate $\\gamma$, decide whether the half-chain entanglement $S(L) \\sim c(\\gamma) \\log L$ persists as $L$ goes to $\\infty$ for $\\gamma$ below some $\\gamma_{c}$, or whether $S$ saturates (area law) for all $\\gamma > 0$ beyond a length $\\ell(\\gamma) \\sim \\exp(C/\\gamma)$. The nonlinear sigma model analysis of Poboiko, Popperl, Gornyi and Mirlin (Phys. Rev. X 13, 041046, 2023) predicts the latter.","problem_ref":null,"references":"","settled_by":"Numerics at system sizes beyond the predicted crossover length, or a rigorous asymptotic analysis of the monitored dynamics.","status_note":"","title":"Does a critical phase exist for monitored free fermions in one 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