{"paper":{"title":"Complexity, Information Geometry, and Loschmidt Echo near Quantum Criticality","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"quant-ph","authors_text":"Mamta Gautam, Nitesh Jaiswal, Tapobrata Sarkar","submitted_at":"2021-10-05T14:54:05Z","abstract_excerpt":"We consider the Nielsen complexity ${\\mathcal C}_N$, the Loschmidt echo ${\\mathcal L}$, and the Fubini-Study complexity $\\tau$ in the transverse XY model, following a sudden quantum quench, in the thermodynamic limit. At small times, the first two are related by ${\\mathcal L} \\sim e^{-{\\mathcal C}_N}$. By computing a novel time-dependent quantum information metric, we show that in this regime, ${\\mathcal C}_N \\sim d\\tau^2$, up to lowest order in perturbation. The former relation continues to hold in the same limit at large times, whereas the latter does not. Our results indicate that in the th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.02099","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/2110.02099/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"}