{"paper":{"title":"Defects and their Time Scales in Quantum and Classical Annealing of the Two-Dimensional Ising Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","cond-mat.stat-mech","hep-lat"],"primary_cat":"quant-ph","authors_text":"Anders W. Sandvik, Na Xu, Phillip Weinberg","submitted_at":"2025-07-12T12:59:40Z","abstract_excerpt":"We investigate defects in the two-dimensional transverse-field Ising ferromagnet on periodic $L\\times L$ lattices after quantum annealing from high to vanishing field. With exact numerical solutions for $L \\le 6$, we observe the expected critical Kibble-Zurek (KZ) time scale $\\propto L^{z+1/\\nu}$ (with $z=1$ and $1/\\nu \\approx 1.59$) at the quantum phase transition. We also observe KZ scaling of the ground-state fidelity at the end of the process. The excitations evolve by coarsening dynamics of confined defects, with a time scale $\\propto L^2$, and interface fluctuations of system-spanning de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09273","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/2507.09273/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"}