{"paper":{"title":"Preconditioned flow as a solution to the hierarchical growth problem in the generalized Lefschetz thimble method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","physics.comp-ph","quant-ph"],"primary_cat":"hep-lat","authors_text":"Atis Yosprakob, Jun Nishimura, Katsuta Sakai","submitted_at":"2024-04-25T13:13:29Z","abstract_excerpt":"The generalized Lefschetz thimble method is a promising approach that attempts to solve the sign problem in Monte Carlo methods by deforming the integration contour using the flow equation. Here we point out a general problem that occurs due to the property of the flow equation, which extends a region on the original contour exponentially to a region on the deformed contour. Since the growth rate for each eigenmode is governed by the singular values of the Hessian of the action, a huge hierarchy in the singular value spectrum, which typically appears for large systems, leads to various technic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16589","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.16589/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}