{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"76c1835357706caa50ef97d944b2b8d7fea986bd6b448dcb94c39f0edb89a8ed","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["441bfa51beac0f3307181ab0085df2798a1893497731a0f0c84c7d8ec867f365","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"247a8428a5aca49b3ed51850f91cdc7be4405a0a50e273a93cd77a6990ad44d3","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":"2","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":"441bfa51beac0f3307181ab0085df2798a1893497731a0f0c84c7d8ec867f365","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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