{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7b0a4bfc232b94f134a43f848bfe61d9d7a8b7a8a1bcc3d8c6b8b33e7a5db6f6","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a4ac3b24db569415cc3d741ba7b669789ec341f03ad07e824a8e1d1861b93178","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.sign-problem-numerics.dynamical-sign-problem","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Simulating how electrons evolve in time requires summing complex phases that cancel more and more as time grows, so the cost rises exponentially with simulated time. For a single magnetic impurity, new methods reduced this to polynomial cost; whether this is possible for whole lattices is open.","posed_since":"","precise":"Real-time diagrammatic and path-integral Monte Carlo for nonequilibrium Green's functions have variance growing as $\\operatorname{exp}(c t)$. Inchworm Monte Carlo (Cohen et al. 2015) and related methods reach polynomial scaling in t for Anderson impurity models. Determine whether a classical algorithm computes local real-time correlators of the infinite 2D Hubbard model at $U/t \\sim 4$, starting from a thermal state at $T \\sim t$, up to time $t_{\\mathrm{max}}$ with error eps at cost polynomial in t_max and 1/eps, or prove that this is hard (e.g. by a complexity reduction). An answer is an algorithm with proven scaling or a hardness proof.","problem_ref":null,"references":"","settled_by":"An algorithm with a proven polynomial cost bound verified against exact results, or a complexity-theoretic reduction showing such an algorithm would imply an unlikely collapse.","status_note":"Polynomial-cost methods exist for quantum impurity models since 2015; no such method is known for lattices.","title":"Polynomial-cost real-time simulation of interacting fermion lattices","topic_ref":"91e71237aaab9c02133089fdeea13d2a6f819a14e160de99c6f929cdb211535a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3aa3308ec11884f917f1766769579cd9607c5179cf7198157322768c02d06862","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"223d2074bbb484e7174947362e0f00cb47aff45fb0ca019911d273b47428b3e0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"NnV-LXjxntwmqQQco0vrq1UJVupuk_B-3mhB5jjEWUFCc2w-_1ohZL2L1cmvqvWD2o8HkFEY5rQc1eYq-hinBA"},"schema":"pubphys.envelope/1"},"record_hash":"3aa3308ec11884f917f1766769579cd9607c5179cf7198157322768c02d06862","leaf_index":1154}